bluuebunny/crossref_metadata_2025 huggingface dataset:
Balayage by Fourier transforms with sparse frequencies in compact abelian torsion groups
Authors: Shapiro George S.
Published: June 2010

Let

Λ
\Lambda

be a discrete subset of a LCA group and E a compact subset of the dual group

Γ
\Gamma

. Balayage is said to be possible for (

Λ
\Lambda

, E) if the Fourier transform of each measure on G is equal on E to the Fourier transform of some measure supported by

Λ
\Lambda

. For a class of infinite compact metrizable

Γ
\Gamma

, including all such torsion groups, we show how to construct

E
⊂
Γ

E \subset \Gamma

such that there are arbitrarily sparse sets

Λ
\Lambda

with balayage possible for (

Λ
\Lambda

, E). E is, moreover, large enough that the set of products

E
⋅
E
⋅
E
=
Γ

E \cdot E \cdot E = \Gamma

.
Local 𝑝-Sidon sets for Lie groups
Authors: Dooley A. H. , Soardi Paolo M.
Published: June 2010

It is shown that a compact Lie group admits no local p-Sidon sets of unbounded degree.
Fuglede’s theorem and limits of spectral operators
Authors: Hadwin Donald W.
Published: June 2010

Suppose K is a compact subset of the plane. A bounded sequence

{

τ
n

}

\{ {\tau _n}\}

of unital homomorphisms from

C
(
K
)

C(K)

into a Banach algebra is pointwise norm convergent if and only if

{

τ
n

(
θ
(
z
)
=
z
)
}

\{ {\tau _n}(\theta (z) = z)\}

is convergent. Applications are made to norm limits of scalar type spectral operators. The proof is based on an asymptotic version of Fuglede’s theorem for Banach algebras.
Resultant operators of a pair of analytic functions
Authors: Gohberg I. C. , Lerer L. E.
Published: June 2010

The well-known results on resultant of polynomials and its continuous analogue is generalized for some classes of analytic functions.
Weak convergence to the fixed point of an asymptotically nonexpansive map
Authors: Bose S. C.
Published: June 2010

It is proved that, in certain Banach spaces, any asymptotically nonexpansive and asymptotically regular map has the property that its iterates, applied to any point in the domain, give a sequence converging weakly to a fixed point.
Rational cobordism operations
Authors: Bendersky Martin
Published: June 2010

Rational cobordism operations dual to the right action are studied. The integral operations, and their compositions are computed in terms of these operations. Similar results for BP-operations are obtained.
Subshifts of finite type in linked twist mappings
Authors: Devaney Robert L.
Published: June 2010

For each pair of nonzero integers j, k, we define a homeomorphism

f

j
,
k

{f_{j,k}}

of the two-disk minus three holes. We show that there exists a compact, invariant, hyperbolic set for each

f

j
,
k

{f_{j,k}}

on which

f

j
,
k

{f_{j,k}}

is conjugate to a subshift of finite type. This implies that the topological entropy of

f

j
,
k

{f_{j,k}}

is bounded below by

4

|

j

|

|

k

|

−
2

|

j

|

−
2

|

k

|

4|j||k| - 2|j| - 2|k|

.
Centralizers of 𝐶¹-diffeomorphisms
Authors: Togawa Yoshio
Published: June 2010

In this paper we prove that

Z
(
f
)
=
{

f
k

|

k
∈
Z
}

Z(f) = \{ {f^k}|k \in Z\}

for generic Axiom A diffeomorphisms. We also prove that generic diffeomorphisms have no k-roots.
Ascent, descent and compact perturbations
Authors: Grabiner Sandy
Published: June 2010

The collections of upper semi-Fredholm operators with finite ascent and of lower semi-Fredholm operators with finite descent are both closed under commuting compact perturbations.
Another approximation theoretic characterization of inner product spaces
Authors: Amir Dan , Deutsch Frank
Published: June 2010

A normed space E is an inner product space if and only if for every 2-dimensional subspace V and every segment

I
⊂
V

I \subset V

, the corresponding metric projections satisfy the commutative property

P
I

P
V

=

P
V

P
I

{P_I}{P_V} = {P_V}{P_I}

.
Solution of planar Diophantine equations
Authors: Owings James C.
Published: June 2010

We continue our investigation, begun in [2], of the “planes” associated with the Diophantine equation
\[

x
2

+

y
2

+

z
2

±
y
z
±
x
z
±
x
y
+
g
x
+
h
y
+
k
z
+
m
=
0.

{x^2} + {y^2} + {z^2} \pm yz \pm xz \pm xy + gx + hy + kz + m = 0.

\]
In particular, we show that the number of planes is finite, thus providing a new way of finding all integral solutions of this equation. Hopefully, our methods will extend to a treatment of the general quadratic equation in three variables.
A criterion for Perron integrability
Authors: Sarkhel D. N.
Published: June 2010

It is shown that a measurable function

f
:
I
=
[
a
,
b
]
→

R
e

f:I = [a,b] \to {R_e}

is necessarily Perron integrable if there exists at least one pair of functions

u
,
l
:
I
→
R

u,l:I \to R

such that (i)

u
(
x
−
)
⩽
u
(
x
)
⩽
u
(
x
+
)

u(x - ) \leqslant u(x) \leqslant u(x + )

and

l
(
x
−
)
⩾
l
(
x
)
⩾
l
(
x
+
)

l(x - ) \geqslant l(x) \geqslant l(x + )

on I, (ii)

I
∖
(

E
1

∪

E
2

)

I\backslash ({E_1} \cup {E_2})

is countable, where
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E 1 equals left-brace x vertical-bar upper D Subscript minus Baseline u left-parenthesis x right-parenthesis greater-than negative normal infinity comma upper D Superscript minus Baseline l left-parenthesis x right-parenthesis greater-than normal infinity right-brace">

E
1

=
{
x

|

D
−

u
(
x
)
>
−
∞
,

D
−

l
(
x
)
>
∞
}

{E_1} = \{ x|{D_ - }u(x) > - \infty ,{D^ - }l(x) > \infty \}

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E 2 equals left-brace x vertical-bar upper D Subscript plus Baseline u left-parenthesis x right-parenthesis greater-than negative normal infinity comma upper D Superscript plus Baseline l left-parenthesis x right-parenthesis greater-than normal infinity right-brace">

E
2

=
{
x

|

D
+

u
(
x
)
>
−
∞
,

D
+

l
(
x
)
>
∞
}

{E_2} = \{ x|{D_ + }u(x) > - \infty ,{D^ + }l(x) > \infty \}

, and (iii)
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="max left-brace right-brace comma times times upper D minus of uu left-parenthesis right-parenthesis x comma times times upper D plus of uu left-parenthesis right-parenthesis x greater-than-or-slanted-equals f left-parenthesis x right-parenthesis greater-than-or-slanted-equals min left-brace right-brace comma times times upper D minus of ll left-parenthesis right-parenthesis x comma times times upper D plus of ll left-parenthesis right-parenthesis x">

max
{

D
−

u
(
x
)
,

D
+

u
(
x
)
}
⩾
f
(
x
)
⩾
min
{

D
−

l
(
x
)
,

D
+

l
(
x
)
}

\max \{ {D_ - }u(x),{D_ + }u(x)\} \geqslant f(x) \geqslant \min \{ {D^ - }l(x),{D^ + }l(x)\}

a.e. on I. In the special case when u and l are respectively major and minor functions of f in the sense of H. Bauer, the result was proved by J. Marcinkiewicz.
Note on the Nevannlinna proximity function
Authors: Lewis John L.
Published: June 2010

Let

λ
\lambda

be a positive function on

(
0
,
∞
)

(0,\infty )

with

lim

r
→
∞

λ
(
r
)
=
∞

{\lim _{r \to \infty }}\lambda (r) = \infty

, and A an arbitrary set of capacity zero. An example is given of a meromorphic function f for which

m
(
r
,
a
)
→
∞
,
r
→
∞

m(r,a) \to \infty ,r \to \infty

, whenever

a
∈
A

a \in A

, and

T
(
r
,
f
)
=
O
[

(
log
⁡
r

)
2

λ
(
r
)
]
,
r
→
∞

T(r,f) = O[{(\log r)^2}\lambda (r)],r \to \infty

.
𝐿²-boundedness for pseudo-differential operators with unbounded symbols
Authors: Childs Gary
Published: June 2010

Kato has proven

L
2

{L^2}

-boundedness if the symbol

a
(
x
,
z
)

a(x,z)

is such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper D Subscript x Superscript beta Baseline upper D Subscript z Superscript alpha Baseline a left-parenthesis x comma z right-parenthesis EndAbsoluteValue less-than-or-slanted-equals left-parenthesis constant right-parenthesis left-parenthesis 1 plus StartAbsoluteValue z EndAbsoluteValue right-parenthesis Superscript left-parenthesis StartAbsoluteValue beta EndAbsoluteValue minus StartAbsoluteValue alpha EndAbsoluteValue right-parenthesis rho">

|

D
x
β

D
z
α

a
(
x
,
z
)

|

⩽
(

constant

)

(
1
+

|

z

|

)

(

|

β

|

−

|

α

|

)
ρ

|D_x^\beta D_z^\alpha a(x,z)|\; \leqslant ({\text {constant}}){(1 + |z|)^{(|\beta | - |\alpha |)\rho }}

for

|

α

|

⩽
[
n

/

2
]
+
1
,

|

β

|

⩽
[
n

/

2
]
+
2

|\alpha | \leqslant [n/2] + 1,|\beta | \leqslant [n/2] + 2

and

0
>
ρ
>
1

0 > \rho > 1

. In this paper,

L
2

{L^2}

-boundedness is shown for a corresponding Hölder continuity condition which requires slightly less smoothness for

a
(
x
,
z
)

a(x,z)

.
On a theorem of Cambern
Authors: Hess H.-U.
Published: June 2010

It is shown that Cambern’s generalized Banach-Stone theorem for spaces of continuous functions on compact sets cannot be extended to the case of spaces of continuous affine functions on simplexes.
A generalization of Singer’s theorem
Authors: Hale Mark P. , Jungnickel Dieter
Published: June 2010

Finite pappian Klingenberg planes and finite desarguesian uniform Hjelmslev planes admit abelian collineation groups acting regularly on the point and line sets; this generalizes Singer’s theorem on finite desarguesian projective planes.
On the inset of a convergence domain
Authors: Kuan Shen Yue
Published: June 2010

Let A be a conservative matrix. The main purpose of this article is to give a negative answer to the open question E raised by Macphail and Wilansky [1], namely, “If

Λ
A
⊥

=

I
A

\Lambda _A^ \bot = {I_A}

, must

Λ
D
⊥

=

I
D

\Lambda _D^ \bot = {I_D}

for every matrix D with

c
D

=

c
A

{c_D} = {c_A}

?".
A selection theorem for multifunctions
Authors: Sarbadhikari H.
Published: June 2010

In this paper the following theorem is proved. X is any set, H is a family of subsets of X which is

λ
\lambda

-additive,

λ
\lambda

-multiplicative and satisfies the

λ
\lambda

-WRP for some cardinal

λ
>

ℵ
0

\lambda > {\aleph _0}

. Suppose Y is a regular Hausdorff space of topological weight

⩽
λ

\leqslant \lambda

such that given any family of open sets, there is a subfamily of cardinality

>
λ

> \lambda

with the same union. Let

F
:
X
→

C

(
Y
)

F:X \to {\mathbf {C}}(Y)

, where

C

(
Y
)

{\mathbf {C}}(Y)

is the family of nonempty compact subsets of Y, satisfy

{
x
:
F
(
x
)
∩
C
≠
∅
}
∈

H

\{ x:F(x) \cap C \ne \emptyset \} \in {\mathbf {H}}

for any closed subset C of Y. Then F admits a

(

H

∩

H

c

)
λ

{({\mathbf {H}} \cap {{\mathbf {H}}^c})_\lambda }

measurable selector.
Alternating basis exchanges in matroids
Authors: Kung Joseph P. S.
Published: June 2010

We study some of the basis exchange properties for matroids implied by the following fact from linear algebra: an alternating multilinear k-form vanishes on any ordered set of k linearly dependent vectors.
Stratifiable 𝜎-discrete spaces are 𝑀₁
Authors: Gruenhage Gary
Published: June 2010

It is shown that stratifiable

σ
\sigma

-discrete spaces are

M
1

{M_1}

. A corollary is that scattered stratifiable spaces are

M
1

{M_1}

.
Even continuity and the Banach contraction principle
Authors: Solomon J. L. , Janos Ludvik
Published: June 2010

In 1967, Philip R. Meyers established a nice converse to the Banach Contraction Mapping Theorem. We provide a counterexample to one of his corollaries and show that if X is a metrizable topological space, f a continuous self-map on X such that: (a)f has a fixed point p which has a compact neighborhood; (b)

f
n

(
x
)
→
p

{f^n}(x) \to p

as

n
→
∞

n \to \infty

for each x in X, then the following are equivalent: (1) f is a contraction relative to a suitable metric on X; (2) the sequence of iterates

{

f
n

}

n
=
1

∞

\{ {f^n}\} _{n = 1}^\infty

is evenly continuous.
A Samelson product and homotopy-associativity
Authors: Schiffman Stephen J.
Published: June 2010

A certain Samelson (commutator) product is computed in the homotopy groups of a finite H-space. This result is applied to the study of H-maps in

π
3

{\pi _3}

of that space, and to the study of multiplications on Lie groups.
An ergodic theorem for Fréchet-valued random variables
Authors: Landers D. , Rogge L.
Published: June 2010

We generalize the classical ergodic theorem from real-valued random variables to Fréchet space-valued random variables and obtain this generalization as a direct corollary of the classical theorem. As an application we obtain several strong laws of large numbers for Fréchet-valued random variables. In a similar way we obtain a martingale theorem for Fréchet-valued random variables.
Constructing sequences of divided powers. II
Authors: Berkson Astrid J. , Newman Kenneth
Published: June 2010

Using principally the exponential and logarithmic Taylor series a number of simple formulas are derived for extending sequences of divided powers in cocommutative irreducible Hopf algebras over fields of characteristic 0. Both the commutative and noncommutative cases are considered.
A characterization of 𝐶*-subalgebras
Authors: van Casteren Jan A.
Published: June 2010

Let A be a closed linear subspace of a

C
∗

{C^\ast }

-algebra B. Adjoin, if necessary, the identity 1 to B. Then A is a

C
∗

{C^\ast }

-subalgebra if and only if, for each x in A, the elements

x
∗

{x^\ast }

and

|

x

|

+
1
−

|

|

x

|

−
1

|

|x| + 1 - ||x| - 1|

are in A. If 1 is in A, then A is a

C
∗

{C^\ast }

-subalgebra if and only if

|

x

|

|x|

is in A for each x in A. Here

|

x

|

|x|

denotes the unique positive square root of

x
∗

x

{x^\ast }x

in B.
Brick decompositions and 𝑄-manifolds
Authors: Curtis D. W. , Kozlowski G.
Published: June 2010

A brick decomposition (respectively, generalized brick decomposition) of a metric space Y is a locally finite, star-finite closed cover

{

Y
α

}

\{ {Y_\alpha }\}

such that each nonempty intersection

Y

α
1

∩
⋯
∩

Y

α
n

,
n
⩾
1

{Y_{{\alpha _1}}} \cap \cdots \cap {Y_{{\alpha _n}}},n \geqslant 1

, is a compact AR (respectively, locally compact AR). Let K be the nerve of the decomposition

{

Y
α

}

\{ {Y_\alpha }\}

, let Q be the Hilbert cube, and

Q
0

=
Q
∖

point
≈
Q
×
[
0
,
1
)

{Q_0} = Q\backslash \;\text {point}\approx Q \times [0,1)

. Then

Y
×
Q
≈

|

K

|

×
Q

Y \times Q \approx |K| \times Q

(respectively,

Y
×

Q
0

≈

|

K

|

×

Q
0

Y \times {Q_0} \approx |K| \times {Q_0}

).
Flat semilattices
Authors: Bulman-Fleming Sydney , McDowell Kenneth
Published: June 2010

Let S (respectively

S

0

{{\mathbf {S}}_0}

) denote the category of all join-semilattices (resp. join-semilattices with 0) with (0-preserving) semilattice homomorphisms. For

A
∈

S

A \in {\mathbf {S}}

let

A
0

{A_0}

represent the object of

S

0

{{\mathbf {S}}_0}

obtained by adjoining a new 0-element. In either category the tensor product of two objects may be constructed in such a manner that the tensor product functor is left adjoint to the hom functor. An object

A
∈

S

(

S

0

)

A \in {\mathbf {S}}\;({{\mathbf {S}}_0})

is called flat if the functor -

−

⊗

S

A
(
−

⊗

S

0

A
)

- { \otimes _{\mathbf {S}}}A( - { \otimes _{{{\mathbf {S}}_0}}}A)

preserves monomorphisms in S

(

S

0

)

({{\mathbf {S}}_0})

. THEOREM. For

A
∈

S

(

S

0

)

A \in {\mathbf {S}}\;({{\mathbf {S}}_0})

the following conditions are equivalent: (1) A is flat in S

(

S

0

)

({{\mathbf {S}}_0})

, (2)

A
0

(
A
)

{A_0}(A)

is distributive (see Grätzer, Lattice theory, p. 117), (3) A is a directed colimit of a system of f.g. free algebras in S

(

S

0

)

({{\mathbf {S}}_0})

. The equivalence of (1) and (2) in S was previously known to James A. Anderson.

(
1
)
⇔
(
3
)

(1) \Leftrightarrow (3)

is an analogue of Lazard’s well-known result for R-modules.
On Galois theory using pencils of higher derivations
Authors: Deveney James K. , Mordeson John N.
Published: June 2010

Let

L
⊃
K

L \supset K

be fields of characteristic

p
≠
0

p \ne 0

. Assume K is the field of constants of a group of pencils of higher derivations on L, and hence L is modular over K and K is separably algebraically closed in L. Every intermediate field F which is separably algebraically closed in L and over which L is modular is the field of constants of a group of pencils of higher derivations if and only if

K
(

L

p
e

)

K({L^{{p^e}}})

has a finite separating transcendence basis over K for some nonnegative integer e. If

p
≠
2
,
3

p \ne 2,3

and

K
(

L

p
e

)

K({L^{{p^e}}})

does have a finite separating transcendence basis over K, and F is the field of constants of a group of pencils, then the group of L over F is invariant in the group of L over K if and only if

F
=
K
(

L

p
r

)

F = K({L^{{p^r}}})

for some nonnegative integer r.
The quasimultiplier conjecture
Authors: McKennon Kelly
Published: June 2010

It is shown by example that the left and right multipliers of a

C
∗

{C^\ast }

-algebra do not always span the linear space of quasi-multipliers.
Power bounded strictly cyclic operators
Authors: Rosenthal Erik J.
Published: June 2010

We show that a power bounded hereditarily strictly cyclic operator on Hilbert space is similar to a contraction. We also show that certain “almost unitary” operators are not strictly cyclic.
Minimal 𝐻² interpolation in the Carathéodory class
Authors: Beller E. , Pinchuk B.
Published: June 2010

For

(

c
1

,
…
,

c
n

)

({c_1}, \ldots ,{c_n})

in

C

n

{{\mathbf {C}}^n}

, let

C
(

c
1

,
…
,

c
n

)

C({c_1}, \ldots ,{c_n})

denote the class of functions
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis equals 1 plus c 1 z plus midline-horizontal-ellipsis plus c Subscript n Baseline z Superscript n Baseline plus normal upper Sigma Subscript k equals n plus 1 Superscript normal infinity Baseline a Subscript k Baseline z Superscript k">

f
(
z
)
=
1
+

c
1

z
+
⋯
+

c
n

z
n

+

Σ

k
=
n
+
1

∞

a
k

z
k

f(z) = 1 + {c_1}z + \cdots + {c_n}{z^n} + \Sigma _{k = n + 1}^\infty {a_k}{z^k}

which are analytic and satisfy

Re
⁡
f
(
z
)
>
0

\operatorname {Re} f(z) > 0

in the unit disc. The unique function of least

H
2

{H^2}

norm in

C
(

c
1

,
…
,

c
n

)

C({c_1}, \ldots ,{c_n})

is explicitly determined.
Inner functions and the maximal ideal space of 𝐻^{∞}(𝑈ⁿ)
Authors: Kon S. H.
Published: June 2010

For the case of the polydisc, Range has shown that the Shilov boundary

∂
n

{\partial _n}

of

H
∞

(

U
n

)

{H^\infty }({U^n})

is a proper subset of

τ

X
n

\tau {X_n}

, the set of all restrictions of complex homomorphisms of

L
∞

(

T
n

)

{L^\infty }({T^n})

to

H
∞

(

U
n

)

{H^\infty }({U^n})

. In this paper, we show that

τ

X
n

\tau {X_n}

is a proper subset of those complex homomorphisms of

H
∞

(

U
n

)

{H^\infty }({U^n})

which are unimodular on the class of all inner functions.
Extreme invariant positive operators on 𝐿_{𝑝}-spaces
Authors: Luschgy Harald
Published: June 2010

Let

(
X
,

A

,
μ
)

(X,\mathfrak {A},\mu )

and

(
Y
,

B

,
ν
)

(Y,\mathfrak {B},\nu )

be finite positive measure spaces. In this note we present characterizations of the extreme points of the convex set of all positive linear operators

T
:

L
p

(
μ
)
→

L
q

(
ν
)

T:{L_p}(\mu ) \to {L_q}(\nu )

with

T

1

X

=

1

Y

T{{\mathbf {1}}_X} = {{\mathbf {1}}_Y}

which are invariant with respect to a semigroup of positive constant preserving contractions on

L
p

(
μ
)
,
1
⩽
p
>
∞
,
1
⩽
q
⩽
∞

{L_p}(\mu ),1 \leqslant p > \infty ,1 \leqslant q \leqslant \infty

.
An extremal problem for functions of positive real part with application to a radius of convexity problem
Authors: Hamilton D. H. , Tuan P. D.
Published: June 2010

The functional
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R e left-brace z p prime left-parenthesis z right-parenthesis slash left-parenthesis p left-parenthesis z right-parenthesis plus beta plus i t right-parenthesis right-brace comma beta greater-than negative 1 comma StartAbsoluteValue z EndAbsoluteValue less-than-or-slanted-equals r comma 0 greater-than r greater-than 1">

Re
⁡
{
z

p
′

(
z
)

/

(
p
(
z
)
+
β
+
i
t
)
}
,
β
>
−
1
,

|

z

|

⩽
r
,
0
>
r
>
1

\operatorname {Re} \{ zp’(z)/(p(z) + \beta + it)\} ,\beta > - 1,|z| \leqslant r,0 > r > 1

, is minimized for all real t over the class of functions of positive real part. The result is applied to obtain the radius of convexity for a family of regular functions.
Longitudes of a link and principality of an Alexander ideal
Authors: Hillman Jonathan A.
Published: June 2010

In this note it is shown that the longitudes of a

μ
\mu

-component homology boundary link L are in the second commutator subgroup G” of the link group G if and only if the

μ
\mu

th Alexander ideal

E

μ

(
L
)

{\mathcal {E}_\mu }(L)

is principal, generalizing the result announced for

μ
=
2

\mu = 2

by R. H. Crowell and E. H. Brown. These two properties were separately hypothesized as characterizations of boundary links by R. H. Fox and N. F. Smythe.
A stronger Borsuk-Ulam type theorem for proper 𝑍_{𝑝}-actions on 𝑚𝑜𝑑𝑝 homology 𝑛-spheres
Authors: Roberts Jean E.
Published: June 2010

We obtain under a less restrictive hypothesis a Borsuk-Ulam type result of Munkholm’s in which the antipodal map is replaced by a

Z
p

{Z_p}

-action on a cohomology n-sphere.
Open book decompositions of 3-manifolds
Authors: Myers Robert
Published: June 2010

We prove that every closed, orientable 3-manifold has an open book decomposition with connected binding. We then give some applications of this result.
On a probabilistic graph-theoretical method
Authors: Nešetřil Jaroslav , Rödl Vojtěch
Published: June 2010

We introduce a method by means of which one can simply prove the existence of sparse hypergraphs with large chromatic number. Moreover this method gives the full solution of an Erdös-Ore problem.
Right alternative algebras and Wedderburn principal theorem
Authors: Thedy Armin
Published: June 2010

Examples are given of right alternative algebras and of quadratic Jordan algebras (the latter only over fields of characteristic two) without a Wedderburn splitting but such that at least one u-isotope admits a Wedderburn splitting. An example of a noncommutative Jordan algebra over a field of characteristic

≠
2

\ne 2

is given such that no u-isotope admits a Wedderburn splitting.
On finite simple groups with a self-centralization system of type (2(𝑛))
Authors: Ferguson Pamela A.
Published: June 2010

Let G denote a simple group with a self-centralization system of type

(
2
(
n
)
)

(2(n))

, where

n
>
3

n > 3

. Let

X
1

{X_1}

denote an exceptional character of G, then

X
1

(
1
)
=
k
n
+
2
ε

{X_1}(1) = kn + 2\varepsilon

where

ε
=
±
1

\varepsilon = \pm 1

. It is known that
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper G EndAbsoluteValue equals n upper X 1 left-parenthesis 1 right-parenthesis left-parenthesis upper X 1 left-parenthesis 1 right-parenthesis minus epsilon right-parenthesis left-parenthesis l n plus 1 right-parenthesis">

|

G

|

=
n

X

1

(
1
)
(

X

1

(
1
)
−
ε
)
(
l
n
+
1
)

|G| = nX_{1}(1)(X_{1}(1)-\varepsilon )(ln + 1)

\]
where l is a nonnegative integer. In this paper G is classified if

l
=
0
,
ε
=
1

l = 0,\varepsilon = 1

and

X
1

(
1
)

{X_1}(1)

is odd.
Rings with subexponential growth and irreducible representations
Authors: Irving Ronald S.
Published: June 2010

Some monoids and algebras are constructed with growth which is subexponential but not polynomially bounded. The algebras have homomorphic images which are primitive with polynomially bounded growth, but which do not satisfy a Nullstellensatz-type of property.
Summability of subsequences and rearrangements of sequences
Authors: Keagy Thomas A.
Published: June 2010

Sufficient conditions have been given that require a matrix A to have the property that every sequence x with a finite limit point have a subsequence y such that each finite limit point of x is a limit point of Ay. In this paper, we show that these conditions may be weakened and obtain an analog in which “subsequence” is replaced with “rearrangement".
Compact dynamical systems
Authors: Knight Ronald A.
Published: June 2010

Compact flows on locally compact phase spaces are characterized in terms of the bilateral stability properties of the orbits and a stability theorem for cycles is formulated.
Sweeping out on a set of integers
Authors: Ellis Martin H. , Friedman Nathaniel A.
Published: June 2010

Let

(
X
,

B

,
m
)

(X,\mathcal {B},m)

be a Lebesgue space,

m
(
X
)
=
1

m(X) = 1

, and let T be an invertible measurable nonsingular aperiodic transformation of X onto X. If S is a set of r integers,

r
⩾
2

r \geqslant 2

, then there exists a set A of measure less than

r

−
1

Σ

k
=
1

r

k

−
1

{r^{ - 1}}\Sigma _{k = 1}^r{k^{ - 1}}

such that

X
=

∪

n
∈
S

T
n

A

X = { \cup _{n \in S}}{T^n}A

. Thus for every infinite set of integers W there exist sets A of arbitrarily small measure such that

X
=

∪

n
∩
W

T
n

A

X = { \cup _{n \cap W}}{T^n}A

.
A note on Segal algebras on Euclidean spaces
Authors: Wang Hwai Chiuan
Published: June 2010

In this note, we construct and study Segal algebras from three important operators on Euclidean spaces - the Hardy-Littlewood maximal function, the Hilbert transform, and the Sobolov operator.
On iterated similarities of operators
Authors: Herrero Domingo A.
Published: June 2010

Let

L

(

H

)

\mathcal {L}(\mathcal {H})

be the algebra of operators on a complex Hilbert space

H

\mathcal {H}

. If

A
∈

L

(

H

)

A \in \mathcal {L}(\mathcal {H})

is invertible and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-brace upper X element-of script upper L left-parenthesis script upper H right-parenthesis colon double-vertical-bar upper A Superscript k Baseline upper X upper A Superscript negative k Baseline double-vertical-bar less-than-or-slanted-equals upper C left-parenthesis upper X right-parenthesis greater-than normal infinity comma k equals 0 comma 1 comma 2 comma ellipsis right-brace">

{
X
∈

L

(

H

)
:

‖

A
k

X

A

−
k

‖

⩽
C
(
X
)
>
∞
,
k
=
0
,
1
,
2
,
…
}

\{ X \in \mathcal {L}(\mathcal {H}):\left \|{A^k}X{A^{ - k}}\right \| \leqslant C(X) > \infty ,k = 0,1,2, \ldots \}

coincides with

L

(

H

)

\mathcal {L}(\mathcal {H})

, then A is a multiple of a similarity of a unitary operator.
Topological mixing of higher degrees
Authors: Goodman Sue , Marcus Brian
Published: June 2010

We give examples of homeomorphisms which are topologically 1-mixing but not topologically 2-mixing. One is a subshift and the other is a diffeomorphism of the torus.
Groups with completely reducible regular representation
Authors: Baggett Larry , Taylor Keith
Published: June 2010

Several examples are constructed of connected Lie groups with completely reducible regular representation. An example is given in each of the following classes: (i) solvable, (ii) amenable, nonsolvable, (iii) nonamenable and (iv) non-Type I. It is also shown by example that G having a completely reducible regular representation does not imply that

A
(
G
)
=

B
0

(
G
)

A(G) = {B_0}(G)

while the reverse implication is known for separable groups (see [2] and [6]).
The uniform continuity of certain translation semigroups
Authors: Johnson Jimmie Lee
Published: June 2010

Let

S
h

f
(
x
)
=
f
(
x
+
h
)

{S_h}f(x) = f(x + h)

for

h
⩾
0

h \geqslant 0

, for

f
∈

L
2

(

R
+

;
K
)

f \in {L^2}({R^ + };K)

, where K is a separable Hilbert space. The translation semigroup

S
h

{S_h}

when restricted to an invariant subspace L is uniformly continuous if and only if

G
L

{G_L}

is an inner function and has an analytic continuation across an open arc of the unit circle at

z
=
1

z = 1

. The operator-valued function

G
L

{G_L}

is associated with the invariant subspace L by Beurling’s theorem.
Properties of 𝑆-closed spaces
Authors: Cameron Douglas E.
Published: June 2010

It is shown that the S-closed spaces introduced by Travis Thompson using semiopen sets may be characterized as spaces where covers by regular closed sets have finite subcovers. S-closed is contagious and semiregular but is neither productive nor preserved by continuous surjections. Extremally disconnected QHC spaces are S-closed and maximal S-closed spaces are precisely the maximal QHC spaces which are extremally disconnected.
On the Sierpiński-Erdős and the Oxtoby-Ulam theorems for some new sigma-ideals of sets
Authors: Mendez C. G.
Published: June 2010

Let

Φ
(
Ψ
)

\Phi (\Psi )

denote the family of subsets of the unit square defined to be of first category (Lebesgue measure zero) in almost every vertical line in the sense of measure (category). Theorem 1. There is a homeomorphism of the unit square onto itself mapping a given set in

Φ
(
Ψ
)

\Phi (\Psi )

) onto a set of Lebesgue measure zero. Theorem 2. There is a set belonging to both

Φ
\Phi

and

Ψ
\Psi

that cannot be mapped onto a set of first category by a homeomorphism of the unit square onto itself. Let C denote the Cantor set, regarded as the product of a sequence of 2-element groups, and let

Λ
\Lambda

denote one of the

σ
\sigma

-ideals of subsets of C studied by Schmidt and Mycielski. Theorem 3. Assuming the continuum hypothesis, the Sierpiński-Erdös theorem holds for

Λ
\Lambda

and the class of subsets of C of Haar measure zero (or of first category). Theorem 4. The Oxtoby-Ulam theorem holds for the image of

Λ
\Lambda

under the Cantor mapping of C onto the unit interval.
A selector for equivalence relations with 𝐺_{𝛿} orbits
Authors: Miller Douglas E.
Published: June 2010

Assume X is a Polish space and E is an open equivalence on X such that every equivalence class is a

G
δ

{G_\delta }

set. We show that there is a

G
δ

{G_\delta }

transversal for E. It follows that for any separable

C
∗

{C^\ast }

-algebra A, there is a Borel cross-section for the canonical map

Irr

(
A
)
→

Prim

(
A
)

{\text {Irr}}(A) \to {\text {Prim}}(A)

.
An elementary proof of the classification of surfaces in the projective 3-space
Authors: Creighton J. H. C.
Published: June 2010

A closed surface embeds in the 3-dimensional real projective space if and only if it is orientable or of odd Euler characteristic. The proof given is elementary in the sense that only geometric techniques are used.
𝑘-regular embeddings of the plane
Authors: Cohen F. R. , Handel D.
Published: June 2010

A map

f
:
X
→

R
n

f:X \to {R^n}

is said to be k-regular if whenever

x
1

,
…
,

x
k

{x_1}, \ldots ,{x_k}

are distinct points of X, then

f
(

x
1

)
,
…
,
f
(

x
k

)

f({x_1}), \ldots ,f({x_k})

are linearly independent. Such maps are of interest in the theory of Cebyšev approximation. In this paper, configuration spaces and homological methods are used to show that there does not exist a k-regular map of

R
2

{R^2}

into

R

2
k
−
α
(
k
)
−
1

{R^{2k - \alpha (k) - 1}}

where

α
(
k
)

\alpha (k)

denotes the number of ones in the dyadic expansion of k. This result is best possible when k is a power of 2.
Karoubi-Villamayor 𝐾-theory is not homotopy Quillen theory
Authors: Strooker Jan R.
Published: June 2010

It is shown that in general the Karoubi-Villamayor group

K

−
2

{K^{ - 2}}

is not a homomorphic image of Milnor’s

K
2

{K_2}

, establishing the title statement.
Minimal primitive ideals of GCR 𝐶*-algebras
Authors: Green Philip
Published: June 2010

We show that a minimal primitive ideal of a GCR algebra may contain the maximal CCR ideal of the algebra, thus giving a negative answer to a question of J. Dixmier.
Isogeny restrictions of irreducible admissible representations are finite direct sums of irreducible admissible representations
Authors: Silberger Allan J.
Published: June 2010

This paper proves that the isogeny restriction of an irreducible admissible representation of a connected reductive algebraic p-adic group decomposes as a finite direct sum of irreducible admissible representations.
A fixed point theorem for image-intersecting mappings
Authors: Abian Alexander
Published: June 2010

Many of the known fixed point theorems of order reversing mappings of partially or simply ordered sets into themselves pertain to dense such ordered sets. In this paper a fixed point theorem is given for an order reversing mapping from a not necessarily dense simply ordered set into itself.
Some remarks on the decomposition of kernels
Authors: Janssen Arnold
Published: June 2010

In a recent paper K. Lange has proved that the decomposition of a stochastic kernel into a continuous and discontinuous part yields kernels again. In the present paper, the author gives a short proof of this theorem and establishes a more general decomposition theorem. Finally, a counter-example shows that in general the Lebesgue decomposition of a kernel does not produce kernels.
Two characterizations of power compact operators
Authors: Tacon D. G.
Published: June 2010

It is shown that if T is an operator on a Banach space with the property that for every bounded sequence

{

x
n

}

\{ {x_n}\}

there is an integer k such that

{

T
k

(

x
n

)
}

\{ {T^k}({x_n})\}

has a convergent subsequence then T is power compact. The equivalent nonstandard characterization is that for each finite point p in an

ℵ
1

{\aleph _1}

-saturated enlargement of the space there is an integer k such that

T
k

p

{T^k}p

is near-standard. Similar results are shown to hold for countable families of operators and for operators possessing weakly compact powers.
𝐿¹(𝐺) as an ideal in its second dual space
Authors: Grosser Michael
Published: June 2010

Based on general results on Banach modules a short proof of the following criterion due to S. Watanabe [5] is given: A group algebra

L
1

(
G
)

{L^1}(G)

is a two-sided ideal in its second dual space (equipped with one of the Arens products) if and only if G is compact.
Pointwise inversion of the spherical transform on 𝐿^{𝑝}(𝐺/𝐾), 1≤𝑝<2
Authors: Stanton Robert J. , Tomas Peter A.
Published: June 2010

The inversion formula for the spherical Fourier transform on a noncompact symmetric space is shown to hold a.e. for

L
p

(
G

/

K
)
,
1
⩽
p
>
2

{L^p}(G/K),1 \leqslant p > 2

.
A multiplication in 𝑁-space
Authors: Lucas Dean
Published: June 2010

A multiplication is constructed which extends the vector space structure of Euclidean n-space to a commutative algebra.
Asymptotic stability of 𝐴𝑠𝑠(𝑀/𝐼ⁿ𝑀)
Authors: Brodmann M.
Published: June 2010

Let R be a noetherian ring, I an ideal of R and M a finitely generated R-module. Let A be the map from N into the subsets of

Spec

(
R
)

{\text {Spec}}(R)

defined by

A
(
n
)
=

Ass
R

(
M

/

I
n

M
)

A(n) = {\text {Ass}_R}(M/{I^n}M)

. We shall prove: (1) For n sufficiently large,

A
(
n
)

A(n)

is independent of n. We moreover give two examples concerning the behavior of

A
(
n
)

A(n)

.
The stable solutions of quadratic matrix equations
Authors: Campbell Stephen , Daughtry John
Published: June 2010

The authors determine which solutions K to the quadratic matrix equation

X
B
X
+
X
A
−
D
X
−
C
=
0

XBX + XA - DX - C = 0

are “stable” in the sense that all small changes in the coefficients of the equation produce equations some of whose solutions are close to K (in the metric determined by the operator norm). Our main result is that a solution is stable if and only if it is an isolated solution. (The isolated solutions already have a simple characterization in terms of the coefficient matrices.) It follows that each equation has only finitely many stable solutions. Equivalently, we identify the stable invariant subspaces for an operator T on a finite-dimensional space as the isolated invariant subspaces.
Extreme points of subclasses of close-to-convex functions
Authors: Silverman H. , Telage D. N.
Published: June 2010

We determine coefficient bounds, distortion and covering theorems, and the extreme points for various subclasses of close-to-convex functions. All results are sharp.
An integrodifferential equation asymptotically of convolution type
Authors: Hannsgen Kenneth B.
Published: June 2010

The resolvent formula is used to study the asymptotic behavior

(
t
→
∞
)

(t \to \infty )

of solution to integrodifferential equations which are close in some sense to equations of convolution type with integrable resolvents.
Fourier series of functions of Λ-bounded variation
Authors: Waterman Daniel
Published: June 2010

It is shown that the Fourier coefficients of functions of

Λ
\Lambda

-bounded variation,

Λ
=
{

λ
n

}

\Lambda = \{ {\lambda _n}\}

, are

O
(

λ
n

/

n
)

O({\lambda _n}/n)

. This was known for

λ
n

=

n

β
+
1

,
−
1
⩽
β
>
0

{\lambda _n} = {n^{\beta + 1}}, - 1 \leqslant \beta > 0

. The classes L and HBV are shown to be complementary, but L and

Λ

BV

\Lambda {\text {BV}}

are not complementary if

Λ

BV

\Lambda {\text {BV}}

is not contained in HBV. The partial sums of the Fourier series of a function of harmonic bounded variation are shown to be uniformly bounded and a theorem analogous to that of Dirichlet is shown for this class of functions without recourse to the Lebesgue test.
On the number of lattice points in a compact 𝑛-dimensional polyhedron
Authors: Tarnopolska-Weiss Marysia
Published: June 2010

An estimate of lattice points, subjected to the orthogonal group

O
(
n
)

O(n)

, is obtained for a compact n-dimensional polyhedron.
A normal first countable ccc nonseparable space
Authors: Bell Murray G.
Published: June 2010

We construct an absolute example of a space having the properties in the title. Let Y be the set of nonempty finite subsets of the Cantor cube of countable weight. The Pixley-Roy topology on Y is not normal, but the Vietoris topology on Y is normal. Our space can be considered a normalization of the Pixley-Roy topology on Y by adding cluster points which as a subspace have the Vietoris topology. The Alexandroff duplicating procedure is used liberally to glue the space together. The example is also a sigma compact paracompact p-space. If further set-theoretic assumptions are made (e.g.

V
=
L

V = L

or

MA

+
¬

CH

{\text {MA}} + \neg {\text {CH}}

), then it is known that even perfectly normal such examples exist.
On 𝐸𝑥𝑡_{𝐾_{*}(𝐾)}(𝜋_{*}(𝐾), 𝐾_{*}(𝑀𝑈))
Authors: Clarke Francis
Published: June 2010

In this note a spectral sequence is constructed which is used to prove the existence of elements of nonzero homological degree in
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E x t Subscript upper K Sub Subscript asterisk Subscript left-parenthesis upper K right-parenthesis Baseline left-parenthesis pi Subscript asterisk Baseline left-parenthesis upper K right-parenthesis comma upper K Subscript asterisk Baseline left-parenthesis upper M upper U right-parenthesis right-parenthesis">

Ext

K
∗

(
K
)

(

π
∗

(
K
)
,

K
∗

(
M
U
)
)

{\operatorname {Ext}_{{K_ \ast }(K)}}({\pi _ \ast }(K), {K_ \ast }(MU))

. Examples of specific elements in terms of representatives in the cobar construction are given.
On projections of finitely additive measures
Authors: Jech Thomas , Prikry Karel
Published: June 2010

A theorem of Z. Frolík and M. E. Rudin states that for every two-valued measure

μ
\mu

on N, if

F
:
N
→
N

F:N \to N

is such that

F
∗

(
μ
)
=
μ

{F_ \ast }(\mu ) = \mu

then

F
(
x
)
=
x

F(x) = x

for almost all x. We prove that a generalization of this theorem fails for measures in general: Theorem. There exist a translation invariant measure

μ
\mu

on N and a function

F
:
N
→
N

F:N \to N

such that

F
∗

(
μ
)
=
μ

{F_ \ast }(\mu ) = \mu

, and if

A
⊆
N

A \subseteq N

is such that F is one-to-one on A, then

μ
(
A
)
⩽

1
2

\mu (A) \leqslant \tfrac {1}{2}

.
A characterization for the product of closed images of metric spaces to be a 𝑘-space
Authors: Tanaka Yoshio
Published: June 2010

We give, under [CH], a necessary and sufficient condition for the product of two closed images of metric spaces to be a k-space.
More paracompact box products
Authors: Roitman Judy
Published: June 2010

We show that if there is no family of cardinality less than c which dominates

ω

ω

^\omega \omega

, then the box product of countably many compact first-countable spaces is paracompact; hence the countable box product of compact metrizable spaces is paracompact if

2
ω

=

ω
2

{2^\omega } = {\omega _2}

. We also give classes of forcing extensions in which many box products are paracompact.
𝑘-regular mappings of 2ⁿ-dimensional Euclidean space
Authors: Chisholm Michael E.
Published: June 2010

A map

f
:
X
→

R
n

f:X \to {R^n}

is said to be k-regular if whenever

x
1

,
…
,

x
k

{x_1}, \ldots ,{x_k}

are distinct points of X, then

f
(

x
1

)
,
…
,
f
(

x
k

)

f({x_1}), \ldots ,f({x_k})

are linearly independent. Using configuration spaces and homological methods, it is shown that there does not exist a k-regular map from

R
n

{R^n}

into

R

n
(
k
−
α
(
k
)
)
+
α
(
k
)
−
1

{R^{n(k - \alpha (k)) + \alpha (k) - 1}}

where

α
(
k
)

\alpha (k)

denotes the number of ones in the dyadic expansion of k and n is a power of 2.
Pseudo-open mappings from topological sums
Authors: Burke Dennis K.
Published: June 2010

Assume S is the free topological sum of spaces

X
1

{X_1}

and

X
2

{X_2}

, on the same set X, and

ϕ
:
S
→
X

\phi :S \to X

is the canonical quotient map. The main result states that X is developable (resp. quasi-developable) if

X
1

{X_1}

and

X
2

{X_2}

are regular developable (resp. quasi-developable) spaces and

ϕ
\phi

is pseudo-open. Examples are given to show that certain topological properties are not preserved under such a construction.
Über endliche Gruppen mit einer zu 𝐿₂(2ⁿ) isomorphen Faktorgruppe
Authors: Baumann Bernd
Published: June 2010

In dieser Arbeit wird die Struktur einer 2-Sylogruppe S einer endlichen Gruppe G beschrieben, für die

G

/

O
2

(
G
)

G/{O_2}(G)

isomorph zu

L
2

(

2
n

)

{L_2}({2^n})

ist und in der keine nichttriviale charakteristische Untergruppe von S normal ist.
Infinite dimensional 𝐿-spaces do not have preduals of all orders
Authors: Armstrong Thomas E.
Published: June 2010

It is shown that if E is an infinite dimensional Banach space with first dual E’, second dual E", and nth dual

E

[
n
]

{E^{[n]}}

and if

E

[
n
]

{E^{[n]}}

is either an L- or M-space all duals are either L- or M-spaces except possibly E which could be a Lindenstrauss space. If E is an L- or M-space there is an integer

n
(
E
)

n(E)

so that if

m
>
n
(
E
)

m > n(E)

there is no Banach space F with

E
=

F

[
m
]

E = {F^{[m]}}

. The linear isomorphic analogues to these isometric results are also established. In particular if E is an

L

1

{\mathcal {L}_1}

or

L

∞

{\mathcal {L}_\infty }

space there is an integer

n
¯

(
E
)

\bar n(E)

so that E is not linearly isomorphic to

F

[
m
]

{F^{[m]}}

for any Banach space F when

m
>

n
¯

(
E
)

m > \bar n(E)

.
A construction of Hilbert spaces of analytic functions
Authors: Hastings William W.
Published: June 2010

A simple technique is presented for constructing a measure

ν
\nu

from a given measure so that

R
2

(
K
,
ν
)

{R^2}(K,\nu )

has certain properties. Here,

R
2

(
K
,
ν
)

{R^2}(K,\nu )

is the closure in

L
2

(
ν
)

{L^2}(\nu )

of the rational functions with poles off K, a compact set containing the support of

ν
\nu

. A typical example shows that there exists a measure

ν
\nu

mutually absolutely continuous with area measure on the unit disk such that

z

\sqrt z

(principal branch) is an element of

R
2

(
K
,
ν
)

{R^2}(K,\nu )

, while each point of the open disk except on the negative real axis is an analytic bounded point evaluation for

R
2

(
K
,
ν
)

{R^2}(K,\nu )

.
Approximation by quotients of rational inner functions
Authors: McDonald John N.
Published: June 2010

Let u be a continuous unimodular function on the n-dimensional torus

T
n

{T^n}

. It is shown that u can be uniformly approximated by quotients of rational inner functions.
Equivalence of norms for coefficients of unitary group representations
Authors: Alesina Alberto
Published: June 2010

We study the equivalence between the

B
(
G
)

B(G)

norm and the supremum norm in the Banach space

A
π

{A_\pi }

, the closed subspace of

B
(
G
)

B(G)

which is generated by the coefficients of a continuous, unitary, irreducible, infinite dimensional representation

π
\pi

of a locally compact, noncompact group G.
Separability and minimal weak base topologies
Authors: Davis S. W. , Stephenson R. M.
Published: June 2010

In this note, we present filter characterizations of minimal weakly first countable, minimal

F

\mathcal {F}

, minimal

F

r

{\mathcal {F}_r}

, weakly first countable-closed,

F

\mathcal {F}

-closed, and

F

r

{\mathcal {F}_r}

-closed spaces. Our main result is a generalization of G. M. Reed’s theorem that every Moore-closed space is separable.
Homogeneity by isotopy
Authors: Garza Gene G.
Published: June 2010

Answered is a question asked by Daverman, Bull. Amer. Math. Soc. 84 (1978), 377-405. It is whether a 2-sphere

Σ
\Sigma

is tame if each isotopy on

Σ
\Sigma

extends to an isotopy of

E
3

{E^3}

?
Simple near-ring centralizers of finite rings
Authors: Maxson Carlton J. , Smith Kirby C.
Published: June 2010

For a finite ring R with identity and a finite unital R-module V we call

C
(
R
)
=
{
f
:
V
→
V

|

f
(
α
v
)
=
α
f
(
v
)

C(R) = \{ f:V \to V|f(\alpha v) = \alpha f(v)

for all

α
∈
R
,
v
∈
V
}

\alpha \in R,v \in V\}

the near-ring centralizer of R. We investigate the structure of

C
(
R
)

C(R)

and obtain a characterization of those rings R for which

C
(
R
)

C(R)

is a simple nonring.
On Fuglede’s theorem and operator topologies
Authors: Rogers Donald D.
Published: June 2010

For each normal operator N and neighborhood E of 0 in the strong or weak operator topology there is a neighborhood D of 0 in the same topology such that

‖
B
‖

⩽
1

\left \| B \right \| \leqslant 1

and

N
B
−
B
N

NB - BN

in D imply

N
∗

B
−
B

N
∗

{N^\ast }B - B{N^\ast }

in E. An example is given to show that D depends on N as well as E.
Amenability of function spaces on thick subsemigroups
Authors: Junghenn H. D.
Published: June 2010

Let F be a translation invariant left introverted algebra of bounded continuous real-valued functions on a semigroup S. Various equivalent versions of the notion of F-left thickness of a subsemigroup T are presented, and the relationship between the left amenability of F and that of

F

|

T

F{|_T}

is examined.
On the norm of the canonical projection of 𝐸*** onto 𝐸^{⊥}
Authors: Johnson Jerry , Wolfe John
Published: June 2010

For each number t with

1
>
t
⩽
2

1 > t \leqslant 2

, a renorming of

c
0

{c_0}

is given for which

‖

I
−
P

‖

=
t

\left \| {I - P} \right \| = t

, where P is the canonical projection of

c
0

∗
∗
∗

c_0^{ \ast \ast \ast }

on

c
0
∗

c_0^\ast

.
Criteria for functions to be of Hardy class 𝐻^{𝑝}
Authors: Yamashita Shinji
Published: June 2010

Let f be holomorphic in the disk

|

z

|

>
1

|z| > 1

. Two criteria (see (I) and (II)) for f to be of

H
2

{H^2}

are extended to the case of

H
p

,
0
>
p
>
+
∞

{H^p},0 > p > + \infty

, by the methods different from known ones for

p
=
2

p = 2

.
Unique ergodicity for certain random translations
Authors: Jamison Benton , Sine Robert
Published: June 2010

Spatially dependent convex combinations of a pair of irrationally related translations on R are shown to admit at most one invariant probability. The only condition on the coefficient functions is measurability and essential positivity.
The unified approach to spectral analysis. II
Authors: Weder R.
Published: June 2010

We apply a new unified method to construct a closed, selfadjoint in

L

2

{\mathcal {L}^2}

, extension of a partial differential operator in all the spaces

L

p

(

R

n

)
,
1
⩽
p
⩽
∞

{\mathcal {L}^p}({{\mathbf {R}}^n}),1 \leqslant p \leqslant \infty

, to a large class of partial differential operators. We obtain very weak conditions in the potentials.
Open nonnegatively curved 3-manifolds with a point of positive curvature
Authors: Elerath Doug
Published: June 2010

Let M be a complete open nonnegatively curved Riemannian 3-manifold with a point at which all sectional curvatures are positive, and suppose that M contains a pole. Then M is not flat on the complement of any compact set. Note that this is clearly false for 2-manifolds.
The Ahlfors estimate
Authors: Fornæss John Erik
Published: June 2010

The Ahlfors estimate gives an upper bound on the growth of a complete Hermitian metric on the punctured unit disc, whose Gaussian curvature is bounded above by

−
1

- 1

. A. Sommese has obtained certain lower bounds on the growth as well. We answer two questions concerning lower bounds, raised by Sommese.
Lower bounds on Herbrand’s theorem
Authors: Statman R.
Published: June 2010

We give non Kalmar-elementary lower bounds on the elimination of quantifier inferences via Herbrand’s theorem.