bluuebunny/crossref_metadata_2025 huggingface dataset:
On a generalized moment problem. II
Authors: Hwang J. S. , Lin G. D.
Published: June 2010

Recently, we have extended the well-known Müntz-Szász theorem by showing that if

f
(
z
)

f(z)

is absolutely continuous and

|

f
′

(
x
)

|

⩾
k
>
0

|f’(x)| \geqslant k > 0

a.e. on

(
a
,
b
)

(a,b)

, where

a
⩾
0

a \geqslant 0

and if

{

n
p

}

\{ {n_p}\}

is a sequence of positive numbers tending to infinity and satisfying

∑

p
=
1

∞

1

/

n
p

=
∞

\sum _{p = 1}^\infty 1/{n_p} = \infty

, then the sequence

{
f

(
x

)

n
p

}

\{ f{(x)^{{n_p}}}\}

is complete on

(
a
,
b
)

(a,b)

if and only if

f
(
x
)

f(x)

is strictly monotone on

(
a
,
b
)

(a,b)

. We now apply Zarecki’s theorem to improve the condition "

|

f
′

(
x
)

|

⩾
k
>
0

|f’(x)| \geqslant k > 0

a.e. on

(
a
,
b
)

(a,b)

" by the condition

f
′

(
x
)
≠
0

f’(x) \ne 0

a.e. on

(
a
,
b
)

(a,b)

". Furthermore, we extend some well-known theorems of Picone, Mikusiński, and Boas.
Boundedness of vector measures with values in the spaces 𝐿₀ of Bochner measurable functions
Authors: Drewnowski Lech
Published: June 2010

Let

L
0

(
Z
)

{L_0}(Z)

be the

F
F

-space of all Bochner measurable functions from a probability space to a Banach space

Z
Z

. We prove that every countably additive vector measure taking values in

L
0

(
Z
)

{L_0}(Z)

has bounded range. This generalizes a recent result due to M. Talagrand and, independently, N. J. Kalton, N. T. Peck and J. W. Roberts, asserting the same for the case when

Z
Z

is the space of scalars.
Necessary conditions for stability of nonsingular endomorphisms of the circle
Authors: Arteaga Carlos
Published: June 2010

In this article we prove that Axiom

A

{\rm {A}}

is a necessary condition for structural stability of

C
1

{C^1}

nonsingular endomorphisms of the circle.
Negative partition relations for ultrafilters on uncountable cardinals
Authors: Kanamori Aki , Taylor Alan D.
Published: June 2010

Assuming GCH, we prove that if

κ
\kappa

is a successor cardinal and

U
U

is a uniform ultrafilter on

κ
\kappa

, then

U
↛

(
U
,
3

)
2

U \nrightarrow {(U,3)^2}

. The case

κ
=

ω
1

\kappa = {\omega _1}

is an old result of Hajnal. Our proof makes use of several known results concerning nonregular, weakly normal and indecomposable ultrafilters, as well as some negative partition relations for uncountable ordinals.
Cremona transformations that are affine automorphisms
Authors: Yoshihara Hisao
Published: June 2010

We present the condition on which a Cremona transformation induces an automorphism of

A

2

{{\mathbf {A}}^2}

.
Completely bounded homomorphisms of operator algebras
Authors: Paulsen Vern I.
Published: June 2010

Let

A
A

be a unital operator algebra. We prove that if

ρ
\rho

is a completely bounded, unital homomorphism of

A
A

into the algebra of bounded operators on a Hilbert space, then there exists a similarity

S
S

, with

‖

S

−
1

‖

⋅

‖
S
‖

=

‖
ρ
‖

c
b

\left \| {{S^{ - 1}}} \right \| \cdot \left \| S \right \| = {\left \| \rho \right \|_{cb}}

, such that

S

−
1

ρ
(
⋅
)
S

{S^{ - 1}}\rho ( \cdot )S

is a completely contractive homomorphism. We also show how Rota’s theorem on operators similar to contractions and the result of Sz.-Nagy and Foias on the similarity of

ρ
\rho

-dilations to contractions can be deduced from this result.
𝐿_{𝑝} smoothness and approximate continuity
Authors: Evans Michael J. , Humke Paul D.
Published: June 2010

It is known that a measurable smooth function can have only countably many points of discontinuity. A measurable function is constructed here having the property of being

L
p

{L_p}

smooth and having uncountably many points of

L
p

{L_p}

(in fact, approximate) discontinuity.
A weighted polynomial inequality
Authors: Lubinsky D. S.
Published: June 2010

In the theory of orthogonal polynomials for weights with noncompact support, much use is made of inequalities relating weighted integrals of polynomials over infinite and finite ranges. Using a short new method of proof, we show such inequalities hold for very general weights in

L
p

{L_p}

and certain Orlicz spaces.
Compact Lie group action and equivariant bordism
Authors: Khare Shabd Sharan
Published: June 2010

Let

G
G

be a compact Lie group and

H
H

a compact Lie subgroup of

G
G

contained in the center of

G
G

with

H
m

{H^m}

the maximal subgroup in the center,

H
H

being

H
H

-boundary. Let

p
r
:

H
m

→
H

pr:{H^m} \to H

be the projection onto the

r
r

th factor and

H
r

{H_r}

be the

r
r

th factor of

H
m

{H^m}

. Let

{

L
r

}

\{ {L_r}\}

be a family of subgroups of

G
G

such that

L
r

∩

H
r

{L_r} \cap {H_r}

is nontrivial. Consider a

G
G

-manifold

M
n

{M^n}

with

p
r
(

G
x

∩

H
m

)

pr({G_x} \cap {H^m})

trivial or containing

L
r

{L_r}

, for every

x
x

in

M
n

{M^n}

. The main result of the paper is that if

∀
x
∈

M
n

\forall x \in {M^n}

,

p
r

(

G
x

∩

H
m

)

{p_r}({G_x} \cap {H^m})

is trivial at least for one

r
r

, then

M
n

{M^n}

is a

G
G

-boundary.
Characterization of dilatations which are expressible as a product of three transvections or three reflections
Authors: Đoković Dragomir Ž.
Published: June 2010

Let

V
V

be a right vector space of dimension at least two over a division ring

K
K

. We characterize the dilatations in

GL

(
V
)

{\text {GL}}(V)

which are expressible as a product of three transvections; these are precisely those dilatations whose ratio is a commutator. Similarly, if char

K
≠
2

K \ne 2

, a dilatation is a product of three reflections if and only if its ratio is a negative of a commutator. The sufficiency of these conditions was established earlier by B. B. Phadke.
The stretched weight lattices of a Weyl group
Authors: Farkas Daniel R.
Published: June 2010

Consider a finite group of automorphisms of a lattice. The nonnegative cone is a fundamental domain (for the action of the group on the lattice) if and only if the group is a Weyl group and the lattice is isomorphic, as a module, to one of the group’s stretched weight lattices.
On the structure of selfadjoint Toeplitz operators with rational matrix symbols
Authors: Rodman Leiba
Published: June 2010

Selfadjoint Toeplitz operators with rational matrix symbols are studied using a general result concerning functions

(
T

(
z

)

−
1

x
,
y
)

(T{(z)^{ - 1}}x,y)

where

T
(
z
)

T(z)

is a polynomial family of Toeplitz operators with rational matrix symbols. It is proved that, apart from a finite number of points, these functions can be continued analytically across the boundary of the resolvent set of

T
(
z
)

T(z)

, for a dense set of

x
x

’s and

y
y

’s. This implies piecewise analyticity of the spectral measure

(
E
x
,
x
)

(Ex,x)

of selfadjoint Toeplitz operators with rational matrix symbol, for a dense set of

x
x

’s.
Compact endomorphisms and closed ideals in Banach algebras
Authors: Grabiner Sandy
Published: June 2010

Every infinite-dimensional Banach algebra with a nonzero compact endomorphism has a proper closed nonzero two-sided ideal. When the algebra is commutative, the ideal is also an ideal in the multiplier algebra.
Local ergodicity of linear contractions on 𝐶(𝑋)
Authors: Bartoszek Wojciech
Published: June 2010

The linear contraction

T
T

on

C

(
X
)

C\left ( X \right )

is locally strongly ergodic if and only if it is continuously scattered and the following condition holds: the support of every extremal (with norm one),

T
∗

{T^ * }

-invariant measure is contained in the set

{

x
:
h

(
x
)

≠
0

}

\left \{ {x:h\left ( x \right ) \ne 0} \right \}

for some continuous function

h
h

which is

T
T

-invariant on the center.
The game-theoretic value and the spectral radius of a nonnegative matrix
Authors: Cohen Joel E. , Friedland Shmuel
Published: June 2010

We relate some minimax functions of matrices to some spectral functions of matrices. If

A
A

is a nonnegative

n
×
n

n \times n

matrix,

υ
(
A
)

\upsilon (A)

is the game-theoretic value of

A
A

, and

ρ
(
A
)

\rho (A)

is the spectral radius of

A
A

, then

υ
(
A
)
≤
ρ
(
A
)

\upsilon (A) \leq \rho (A)

. Necessary and sufficient conditions for

υ
(
A
)
=
ρ
(
A
)

\upsilon (A) = \rho (A)

are given. It follows that if

A
A

is nonnegative and irreducible and

n
>
1

n > 1

, then

υ
(
A
)
>
ρ
(
A
)

\upsilon (A) > \rho (A)

. Also, if, for a real matrix

A
A

and a positive matrix

B
B

,
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upsilon left-parenthesis upper A comma upper B right-parenthesis equals sup Underscript upper X Endscripts inf Underscript upper Y Endscripts upper X Superscript upper T Baseline upper A upper Y slash upper X Superscript upper T Baseline upper B upper Y">

υ
(
A
,
B
)
=

sup
X

inf
Y

X
T

A
Y

/

X
T

B
Y

\upsilon (A,B) = {\sup _X}{\inf _Y}{X^T}AY/{X^T}BY

over probability vectors

X
X

and

Y
Y

, then for nonnegative, nonsingular

A
A

and positive

B
B

,

ρ
(
A
B
)
=

[
υ
(

A

−
1

,
B
)

]

−
1

\rho (AB) = {[\upsilon ({A^{ - 1}},B)]^{ - 1}}

.
Integrability of power series
Authors: Ram Babu
Published: June 2010

The object of this paper is to obtain generalization of certain results of Jain [3] and Woyczynski [5] concerning integrability of power series.
Continuous functions on polar sets
Authors: Jesuraj Ramasamy
Published: June 2010

Let

Ω
\Omega

be a second countable Brelot harmonic space with a positive potential. If

K
K

is a compact subset of

Ω
\Omega

with more than one point, then

K
K

is a polar set iff every positive continuous function on

K
K

can be extended to a continuous potential on

Ω
=

R

n

(
n
⩾
3
)

\Omega = {{\mathbf {R}}^n}(n \geqslant 3)

. This is a generalization of the result proved by H. Wallin for the special case

Ω
=

R

n

(
n
⩾
3
)

\Omega = {{\mathbf {R}}^n}(n \geqslant 3)

with Laplace harmonic space.
A uniqueness condition for sequences
Authors: Leth Steven
Published: June 2010

Under certain conditions a sequence of real numbers converging to zero is determined up to a constant multiple by the comparisons of its subsums. One such condition is that each number in the sequence be majorized by the sum of the elements beyond it.
On the preservation of determinacy under convolution
Authors: Berg Christian
Published: June 2010

In 1959 Devinatz remarked that if

μ
∗
ν

\mu *\nu

is a determinate measure on the real line, then so are

μ
\mu

and

ν
\nu

. It is shown here how this follows from a theorem of M. Riesz, and also how it can be extended to

d
d

dimensions. Recently Diaconis raised the question whether the converse is true. We answer this in the negative by producing a determinate measure

ν
\nu

on the real line such that

ν
∗
ν

\nu *\nu

is indeterminate. The relation to previous work of Heyde and to the condition of Carleman is discussed.
A unique decomposition of involutions of handlebodies
Authors: Nelson Roger B.
Published: June 2010

We consider a PL involution of an orientable,

3
3

-dimensional handlebody for which each component of the fixed point set is

2
2

-dimensional. The handlebody is uniquely equivariantly decomposed as a disk sum of handlebodies

M
i

{M_i}

such that if

M
i

≈

A
i

×
I

{M_i} \approx {A_i} \times I

, then

h

|

M
i

h|{M_i}

is equivalent to (i)

α
×

i

d

I

\alpha \times {\text {i}}{{\text {d}}_I}

, where

α
\alpha

is an involution of

A
A

, or to (ii)

i

d

a

×
r

{\text {i}}{{\text {d}}_a} \times r

, where

r
(
t
)
=
−
t

r(t) = - t

for all

t
∈
I
=
[
−
1
,
1
]

t \in I = [ - 1,1]

.
Finite operators and similarity orbits
Authors: Fialkow Lawrence A. , Herrero Domingo A.
Published: June 2010

In this note we answer the question of J. P. Williams as to which Hilbert space operators

T
T

have the property that every similarity transformation

W

−
1

T
W

{W^{ - 1}}TW

is a finite operator:

T
T

has this property if and only if its image in the Calkin algebra satisfies a quadratic equation.
Which amalgams are convolution algebras?
Authors: Stewart James , Watson Saleem
Published: June 2010

We determine necessary and sufficient conditions on a locally compact abelian group

G
G

for the amalgam

(

L
p

,

l
q

)

(
G
)

\left ( {{L^p},{l^q}} \right )\left ( G \right )

to be an algebra under convolution. If

q
>
1
,
G

q > 1,G

must be compact; if

p
>
1
,
G

p > 1,G

must be discrete. If

p
⩾
1

p \geqslant 1

and

q
⩽
1

q \leqslant 1

, the amalgam is always an algebra.
Linear maps do not preserve countable dimensionality
Authors: Bestvina Mladen , Mogilski Jerzy
Published: June 2010

Examples of linear maps between normed spaces are constructed, including a one-to-one map from a countable-dimensional linear subspace of

l
2

{l_2}

onto

l
2

{l_2}

. We prove that the linear span of a countable-dimensional linearly independent subset of a normed linear space is, in many cases, countable dimensional.
Partitions of unity and approximation
Authors: de Boor C. , DeVore R.
Published: June 2010

We show that for certain translation invariant spaces

S
S

, a necessary and sufficient condition for the eventual denseness of the corresponding scaled spaces

S
h

{S_h}

is that

S
S

contain a stable and locally supported partition of unity. These results have been motivated by recent work on approximation by multivariate piecewise polynomials on regular meshes.
Translation-invariant linear forms on 𝐿_{𝑝}(𝐺)
Authors: Rosenblatt Joseph
Published: June 2010

Let

G
G

be a compact group such that the identity representation of

G
G

is not contained in the regular representation on

L
2
0

(
G
,

λ
G

)

L_2^0(G,{\lambda _G})

of

G
G

with the discrete topology. Then any left translation invariant linear form on

L
p

(
G
)
,
1
>
p
>
∞

{L_p}(G),1 > p > \infty

, is continuous and must be a constant times the Haar integral. This shows that many classical matrix groups

G
G

admit only continuous left translation invariant linear forms on

L
p

(
G
)
,
1
>
p
>
∞

{L_p}(G),1 > p > \infty

.
A local characterization of Noetherian and Dedekind rings
Authors: Lequain Yves
Published: June 2010

Let

R
R

be a ring and

M
M

a maximal ideal of

R
R

. Then

R
R

is Noetherian if and only if every ideal contained in

M
M

is finitely generated;

R
R

is Dedekind if and only if every nonzero ideal contained in

M
M

is invertible.
Short normal paths and spectral variation
Authors: Bhatia Rajendra , Holbrook John A. R.
Published: June 2010

We introduce the notion of a "short normal path" between matrices

S
S

and

T
T

, that is, a continuous path from

S
S

to

T
T

consisting of normal matrices and having the same length as the straight line path from

S
S

to

T
T

. By this means we prove that for certain normal matrices

S
S

and

T
T

the eigenvalues of

S
S

and

T
T

may be paired in such a way that the maximum distance (in the complex plane) between the pairs is no more than the operator norm

‖

S
−
T

‖

\left \| {S - T} \right \|

. In particular, we generalize and provide a new approach to a recent result of Bhatia and Davis treating the case of unitary

S
S

and

T
T

.
Totally real embeddings of 𝑆³ in 𝐶³
Authors: Ahern Patrick , Rudin Walter
Published: June 2010

An explicit totally real embedding of

S
3

{S^3}

in

C

3

{{\text {C}}^3}

is exhibited. It has the form

F
(
z
,
w
)
=
(
z
,
w
,
P
(
z
,
w
)
)

F(z,w) = (z,w,P(z,w))

where

P
P

is a (nonholomorphic) polynomial of degree 4, and

(
z
,
w
)

(z,w)

ranges over the unit sphere in

C

2

{{\text {C}}^2}

.
Eventual disconjugacy of a linear differential equation. II
Authors: Trench William F.
Published: June 2010

A sufficient condition is given for eventual disconjugacy of an

n
n

th-order linear differential equation. The condition is weaker than one given in an earlier paper with the same title, and the conclusion is sharper.
Function spaces of low Borel complexity
Authors: Dijkstra J. , Grilliot T. , Lutzer D. , van Mill J.
Published: June 2010

In this paper we investigate situations in which the space

C
π

(
X
)

{C_\pi }(X)

of continuous, real-valued functions on

X
X

is a Borel subset of the product space

R

X

{{\mathbf {R}}^X}

. We show that for completely regular, nondiscrete spaces,

C
π

(
X
)

{C_\pi }(X)

cannot be a

G
δ

{G_\delta }

, an

F
σ

{F_\sigma }

, or a

G

δ
σ

{G_{\delta \sigma }}

subset of

R

X

{{\mathbf {R}}^X}

, but it can be an

F

σ
δ

{F_{\sigma \delta }}

or

G

δ
σ
δ

{G_{\delta \sigma \delta }}

subset.
The Hurewicz image of Ray’s elements in 𝑀𝑆𝑝_{∗}
Authors: Kochman Stanley O.
Published: June 2010

In this paper we determine an explicit formula for the symplectic Hurewicz homomorphism of Nigel Ray’s sequence of torsion elements in the symplectic bordism ring.
On relative normal complements in finite groups. III
Authors: Leonard Henry S.
Published: June 2010

Let

G
G

be a finite group, let

H
≤
G

H \leq G

, and let

π
\pi

be the set of prime divisors of

|
H
|

\left | H \right |

. Assume that whenever two elements of

H
H

are

G
G

-conjugate then they are

H
H

-conjugate. Assume that for all

h
∈

H
#

h \in {H^\# }

,

(

C
G

(
h
)
:

C
H

(
h
)
)

({C_G}(h):{C_H}(h))

is a

π
′

\pi ’

-number. We prove that

H
H

is a

π
\pi

-Hall subgroup and that there exists a normal complement

G
0

=
G
−

(

H
#

)

G
,
π

{G_0} = G - {({H^\# })^{G,\pi }}

. An example shows that the generalization to relative normal complements is not true.
A note on intersection of lower semicontinuous multifunctions
Authors: Lechicki Alojzy , Spakowski Andrzej
Published: June 2010

Let

F
1

{F_1}

and

F
2

{F_2}

be closed and convex valued multifunctions from a topological space

X
X

to a normed space

Y
Y

. Assume that the multifunctions are lower semicontinuous at

x
0

{x_0}

. We proof that the intersection multifunction

F
=

F
1

∩

F
2

F = {F_1} \cap {F_2}

is lower semicontinuous at

x
0

{x_0}

provided

F
(

x
0

)

F({x_0})

is bounded and has nonempty interior.
On representations of the holomorph of analytic groups
Authors: Lee Dong Hoon
Published: June 2010

We completely characterize those complex analytic groups whose holomorph groups admit finite-dimensional faithful complex analytic representations.
The proof of a conjecture of Graham for sequences containing primes
Authors: Klein Rivka
Published: June 2010

Let

a
1

>

a
2

>
⋯
>

a
n

{a_1} > {a_2} > \cdots > {a_n}

be a finite sequence of positive integers. R. L. Graham has conjectured that

max

i
,
j

{

a
i

/

(

a
i

,

a
j

)

}

⩾
n

{\max _{i,j}}\left \{ {{a_i}/({a_i},{a_j})} \right \} \geqslant n

. We verify this conjecture in case at least one of the

α
i

{\alpha _i}

’s is prime.
SLLN and convergence rates for nearly orthogonal sequences of random variables
Authors: Móricz Ferenc
Published: June 2010

Let

{

X
k

:
k
⩾
1
}

\{ {X_k}:k \geqslant 1\}

be a sequence of random variables with finite second moments

E

X
k
2

=

σ
k
2

>
∞

EX_k^2 = \sigma _k^2 > \infty

for which
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue upper E upper X Subscript k Baseline upper X Subscript l Baseline EndAbsoluteValue less-than-or-slanted-equals sigma Subscript k Baseline sigma Subscript l Baseline rho left-parenthesis StartAbsoluteValue k minus l EndAbsoluteValue right-parenthesis">

|

E

X
k

X
l

|

⩽

σ
k

σ
l

ρ
(

|

k
−
l

|

)

|E{X_k}{X_l}| \leqslant {\sigma _k}{\sigma _l}\rho (|k - l|)

, where

{
ρ
(
j
)
:
j
⩾
0
}

\{ \rho (j):j \geqslant 0\}

is a sequence of nonnegative numbers with

∑

j
=
0

∞

ρ
(
j
)

>
∞

\sum \nolimits _{j = 0}^\infty {\rho (j)} > \infty

. In particular, in the case of orthogonality,

ρ
(
j
)
=
0

\rho (j) = 0

for

j
⩾
1

j \geqslant 1

. We prove strong laws for the first arithmetic means

ζ
n

=

n

−
1

∑

k
=
1

n

X
k

{\zeta _n} = {n^{ - 1}}\sum \nolimits _{k = 1}^n {{X_k}}

and the Cesàro means
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="tau Subscript n Baseline equals n Superscript negative 1 Baseline sigma-summation Underscript k equals 1 Overscript n Endscripts left-parenthesis 1 minus left-parenthesis k minus 1 right-parenthesis n Superscript negative 1 Baseline right-parenthesis upper X Subscript k Baseline period">

τ
n

=

n

−
1

∑

k
=
1

n

(
1
−
(
k
−
1
)

n

−
1

)

X
k

.

{\tau _n} = {n^{ - 1}}\sum \limits _{k = 1}^n {(1 - (k - 1){n^{ - 1}}){X_k}} .

\]
The convergence rates are studied in the form

P
{

sup

n
>

2
p

|

ζ
n

|

>
ε
}

P\{ {\sup _{n > {2^p}}}|{\zeta _n}| > \varepsilon \}

and

P
{

sup

n
>

2
p

|

τ
n

|

>
ε
}

P\{ {\sup _{n > {2^p}}}|{\tau _n}| > \varepsilon \}

, where

ε
>
0

\varepsilon > 0

is fixed and

p
p

tends to

∞
\infty

. At the end, the case where

Σ

j
=
0

∞

ρ
(
j
)
=
∞

\Sigma _{j = 0}^\infty \rho (j) = \infty

is also treated.
Classification of semicrossed products of finite-dimensional 𝐶*-algebras
Authors: DeAlba Luz M. , Peters Justin
Published: June 2010

LetA\mathfrak {A},B\mathfrak {B}be finite-dimensionalC∗{C^*}-algebras with automorphismsα\alpha,β\beta, respectively. Then the semicrossed productsZ+×αA{{\mathbf {Z}}^ + }{ \times _\alpha }\mathfrak {A},Z+×βB{{\mathbf {Z}}^ + }{ \times _\beta }\mathfrak {B}are isomorphic iff there is an isomorphismψ:A→B\psi :\mathfrak {A} \to \mathfrak {B}and a unitaryU∈BU \in \mathfrak {B}such thatβ∘ψ=(Ad⁡U)ψ∘α\beta \circ \psi = (\operatorname {Ad} U)\psi \circ \alpha.
Primitive noncommutative Jordan algebras with nonzero socle
Authors: Lopez Antonio Fernandez , Palacios Angel Rodriguez
Published: June 2010

Let

A
A

be a nondegenerate noncommutative Jordan algebra over a field

K
K

of characteristic

≠
2

\ne 2

. Defining the socle

S
(
A
)

S(A)

of

A
A

to be the socle of the plus algebra

A
+

{A^ + }

, we prove that

S
(
A
)

S(A)

is an ideal of

A
A

; then we prove that if

A
A

has nonzero socle,

A
A

is prime if and only if it is primitive, extending a result of Osborn and Racine [6] for the associative case. We also describe the prime noncommutative Jordan algebras with nonzero socle and in particular the simple noncommutative Jordan algebras containing a completely primitive idempotent. In fact we prove that a nondegenerate prime noncommutative Jordan algebra with nonzero socle is either (i) a noncommutative Jordan division algebra, (ii) a simple flexible quadratic algebra over an extension of the base field, (iii) a nondegenerate prime (commutative) Jordan algebra with nonzero socle, or (iv) a

K
K

-subalgebra of

L
W

(
V

)

(
λ
)

{L_W}{(V)^{(\lambda )}}

containing

F
W

(
V
)

{F_W}(V)

or of

H

(

L
V

(
V
)
,
∗

)

(
λ
)

H{({L_V}(V), * )^{(\lambda )}}

containing

H
(

F
V

(
V
)
,
∗
)

H({F_V}(V), * )

where in the first case

(
V
,
W
)

(V,W)

is a pair of dual vector spaces over an associative division

K
K

-algebra

D
D

and

λ
≠
1

/

2

\lambda \ne 1/2

is a central element of

D
D

, and where in the second case

V
V

is self-dual with respect to an hermitian inner product

(

|

)
,
D

(|),D

has an involution

α
→

α
¯

\alpha \to \bar \alpha

and

λ
≠
1

/

2

\lambda \ne 1/2

is a central element of

D
D

with

λ
+

λ
¯

=
1

\lambda + \bar \lambda = 1

.
Large-time behavior of solutions to certain quasilinear parabolic equations in several space dimensions
Authors: Bauman Patricia , Phillips Daniel
Published: June 2010

We consider the Cauchy problem,

u
t

+

div

f
(
u
)
=
Δ
u

{u_t} + {\text {div}}f(u) = \Delta u

for

x
∈

R

n

,
t
>
0

x \in {{\mathbf {R}}^n},t > 0

with

u
(
x
,
0
)
=

u
0

(
x
)

u(x,0) = {u_0}(x)

. For

n
=
1

n = 1

, suppose

f
>
0

f > 0

and

∫

|

u
0

−
ϕ

|

d
x
>
∞

\smallint \left | {{u_0} - \phi } \right |dx > \infty

where

ϕ
\phi

is piecewise constant and

ϕ
(
x
)
→

u
+

(

u
−

)

\phi (x) \to {u^ + }({u^ - })

as

x
→
+
∞
(
−
∞
)

x \to + \infty ( - \infty )

. A result of Il’in and Oleinik states that if

ϕ
(
x
−
k
t
)

\phi (x - kt)

is an entropy solution of

u
t

+

div

f
(
u
)
=
0

{u_t} + {\text {div}}f(u) = 0

, then

u
(
x
,
t
)

u(x,t)

approaches a traveling wave solution,

u
~

(
x
−
k
t
)

\tilde u(x - kt)

, as

t
→
∞

t \to \infty

, with

u
~

(
x
)
→

u
+

(

u
−

)

\tilde u(x) \to {u^ + }({u^ - })

as

x
→
+
∞
(
−
∞
)

x \to + \infty ( - \infty )

. We give two examples which show that this result does not hold for

n
⩾
2

n \geqslant 2

.
Two exact sequences in rational homotopy theory relating cup products and commutators
Authors: Lambe Larry A.
Published: June 2010

Let

X
X

be an

(
n
−
1
)

(n - 1)

-connected topological space of finite rational type (i.e.

H
n

(
X
;
Q
)

{H_n}(X;Q)

is finite dimensional over

Q
Q

for all

n
n

). Sullivan’s notion of minimal model is used to derive two exact sequences involving the kernel of the cup product operation in dimension

n
n

and Whitehead products. The first of these generalizes both a theorem of John C. Wood [JCW] and a theorem of Dennis Sullivan [DS] and states that the kernel of the cup product map

H
1

(
X
)
∧

H
1

(
X
)
→

H
2

(
X
)

{H^1}(X) \wedge {H^1}(X) \to {H^2}(X)

is rationally the dual of the second factor of the lower central series of the fundamental group. Other examples are given in the last section.
Boundary behavior of Green potentials
Authors: Luecking Daniel H.
Published: June 2010

A Green potential on the unit disk

{

|
z
|

>
1
}

\{ \left | z \right | > 1\}

is a function

u
(
z
)

u(z)

of the form
\[

u
(
z
)
=
∫

log
⁡

|

1
−

w
¯

z

z
−
w

|

 

d
α
(
w
)
,

u(z) = \int {\log \left | {\frac {{1 - \bar wz}}{{z - w}}} \right |{\text { }}} d\alpha (w),

\]
where

α
\alpha

is a positive measure such that

∫
(
1
−

|
w
|

)
d
α
(
w
)

\smallint (1 - \left | w \right |)d\alpha (w)

is finite. In this note I give a necessary and sufficient condition on a relatively closed subset

F
F

of the unit disk in order that, for all such

u
(
z
)

u(z)

,
\[

lim inf

F
∋
z
→
1

(
1
−

|
z
|

)
u
(
z
)
=
0.

\liminf _{F \ni z \to 1} (1 - \left | z \right |) u(z) = 0.

\]
The condition is that the hyperbolic capacity of the portion of

F
F

in arbitrarily small neighborhoods of 1 is bounded away from zero.
The moments of certain complex potentials
Authors: Fegan Howard D. , Gilkey Peter B.
Published: June 2010

Let

M
M

be a compact homogeneous space, let

Δ
\Delta

be the Laplacian, and let

V
V

be the vector space of Fegan potentials. If

q
∈
V

q \in V

, then

Δ
\Delta

and

Δ
+
q

\Delta + q

have the same spectrum. We show that all the moments of such a potential must vanish.
Counterexample to the spectral mapping theorem for the exponential function
Authors: Hejtmanek J. , Kaper Hans G.
Published: June 2010

An example is given of an unbounded operator in a Hilbert space which generates a strongly continuous semigroup and for which the spectral mapping theorem for the exponential function does not hold. The spectra of both the generator and the semigroup are determined explicitly.
Stable rank of the disc algebra
Authors: Jones P. W. , Marshall D. , Wolff T.
Published: June 2010

We prove that the Bass stable rank of the disc algebra is one.
An example of Fréchet space, not Montel, without infinite-dimensional normable subspaces
Authors: Díaz Juan C.
Published: June 2010

Given

X
X

a Fréchet Montel space, no infinite dimensional subspace of

X
X

is normable. We show that the converse implication is not true in general. In fact we provide here a Fréchet space

X
X

(moreover,

X
X

is a perfect Fréchet space), which is not Montel but does not contain an infinite dimensional normable subspace.
On nonlinear evolution operators associated with some nonlinear dispersive equations
Authors: Oharu Shinnosuke , Takahashi Tadayasu
Published: June 2010

The initial-boundary value problem for a nonlinear dispersive system with time-dependent boundary condition is discussed in the Sobolev space

H
1

{H^1}

from the point of view of the theory of nonlinear evolution operators. A notion of weak solution to the problem is introduced and the associated family of solution operators is constructed in such a way that it gives rise to a nonlinear evolution operator with time-dependent domain. Various qualitative properties as well as regularity of the weak solutions are investigated through those of the constructed evolution operator.
On a conjecture of Zassenhaus on torsion units in integral group rings. II
Authors: Polcino Milies César , Ritter Jürgen , Sehgal Sudarshan K.
Published: June 2010

Suppose that a group

G
G

has a normal subgroup

C
C

where

C
C

and

G

/

C

G/C

are cyclic of relatively prime orders. Then any torsion unit in

Z
G

ZG

is rationally conjugate to a trivial unit.
Existence of best 𝑛-convex approximations
Authors: Zwick D.
Published: June 2010

We prove that every function

f
f

, continuous on a compact interval

[
a
,
b
]

[a,b]

, has a continuous, best

n
n

-convex approximation with respect to the uniform norm on

[
a
,
b
]

[a,b]

.
Multiple images and local times of measurable functions
Authors: Berman Simeon M.
Published: June 2010

Let

x
(
t
)

x(t)

,

0
≤
t
≤
1

0 \leq t \leq 1

, be a real-valued measurable function having a local time

α

[
0
,
t
]

(
x
)

{\alpha _{[0,t]}}(x)

which is continuous in

t
t

, for almost all

x
x

. Then, for every integer

m
≥
2

m \geq 2

, and every nonempty open subinterval

J
⊂
[
0
,
1
]

J \subset [0,1]

, there exist

m
m

disjoint subintervals

I
1

,
…
,

I
m

⊂
J

{I_1}, \ldots ,{I_m} \subset J

such that the intersection of the images of

I
1

,
…
,

I
m

{I_1}, \ldots ,{I_m}

under the mapping

t
→
x
(
t
)

t \to x(t)

has positive Lebesgue measure. The result applies to a large class of sample functions of stochastic processes, and also to multidimensional

t
t

and

x
(
⋅
)

x( \cdot )

.
Concerning the function equation 𝑓(𝑔)=𝑓, regular mappings and periodic mappings
Authors: Young Sam W.
Published: June 2010

Under certain conditions on the space

X
X

, given

f
:
X
↠
Y

f:X \twoheadrightarrow Y

is light and

g
:
X
↠
X

g:X \twoheadrightarrow X

, the equation

f
(
g
)
=
f

f(g) = f

yields only periodic solutions for

g
g

.
On the formal groups approach to cobordism
Authors: Buoncristiano Sandro , Hacon Derek
Published: June 2010

We give a direct proof of the fact that the complex bordism ring

U
∗

{U_ * }

is a polynomial ring, based on Quillen’s approach. The proof is self-contained, apart from the assumption that the groups

U
n

{U_n}

are all finitely generated and an algebraic lemma on formal groups.
𝐿𝑈-factorization of operators on 𝑙₁
Authors: Andrews Kevin T. , Smith Philip W. , Ward Joseph D.
Published: June 2010

Necessary and sufficent conditions are obtained for LU-factorization of operators on

l
1

{l_1}

. In particular it is shown that uniform invertibility of the compressions of the operator is not sufficient to insure an LU-factorization of the operator, thus answering a question of de Boor, Jia, and Pinkus.
A characterization of harmonic foliations by variations of the metric
Authors: Hvidsten Michael D. , Tondeur Philippe
Published: June 2010

In this paper it is shown that a harmonic Riemannian foliation of a Riemannian manifold can be characterized as being a critical point of the energy of the foliation under certain variations of the manifold’s Riemannian metric. These variations are those induced by the flows of vector fields on the manifold.
Monotone gradients on Banach lattices
Authors: Sundaresan K.
Published: June 2010

It is well known that a differentiable real valued function on the real line is convex iff its derivative is nondecreasing. This characterization of differentiable convex functions does not extend if the domain of the function is a Banach lattice of

dim
⩾
2

\dim \geqslant 2

. In this paper a complete characterization of a subclass of differentiable convex functions on a given Banach lattice is obtained in terms of the monotonicity and natural orthogonality properties of the gradients. It is well known that a differentiable real valued function on the real line is convex iff its derivative is nondecreasing. It is also known that a

C
1

{C^1}

-real valued function

F
F

on an arbitrary Banach space

E
E

is convex iff the gradient of

F
F

, say

f
f

, satisfies the condition (*)

(
f
(
x
)
−
f
(
y
)
,
x
−
y
)
⩾
0

(f(x) - f(y),x - y) \geqslant 0

for all

x
x

,

y
∈
E

y \in E

. Condition (*) is referred to in the literature as a monotonicity condition. However when

E
E

is a Banach lattice, it is natural to define a function

f
f

on

E
E

into another Banach lattice

E
1

{E_1}

as nondecreasing if

f
(
x
)
⩾
f
(
y
)

f(x) \geqslant f(y)

whenever

x
x

,

y
y

in

E
E

are such that

x
⩾
y

x \geqslant y

. The present investigation originated out of the surprising fact that, as shown by suitable examples, the characterization of

C
1

{C^1}

-convex real valued functions on the real line recalled above, does not extend if the domain of the function is a Banach lattice of

dim
⩾
2

\dim \geqslant 2

, and the monotonicity of the gradient function is interpreted as in the preceding sentence. More specifically, if

E
E

is a Banach lattice of

dim
⩾
2

\dim \geqslant 2

, there are

C
1

{C^1}

-convex real valued functions on

E
E

with gradients not nondecreasing and there are

C
1

{C^1}

-real valued functions on

E
E

with gradients nondecreasing which fail to be convex. The main result here provides a complete characterization of

C
1

{C^1}

-convex real valued functions

Φ
\Phi

on an arbitrary Banach lattice

E
E

of which the translates

Φ
(
x
+
y
)
−
Φ
(
x
)

\Phi (x + y) - \Phi (x)

are orthogonally additive in

y
y

for all

x
x

in

E
E

, in terms of the monotonicity and natural orthogonality properties of the gradient map of

Φ
\Phi

. The characterization of the special class of

C
1

{C^1}

-convex functions on Banach lattices stated in the main result here appears to be a reasonable substitute of the characteristic property of

C
1

{C^1}

-convex real valued functions on the real line recalled above. The plan of the paper is as follows. In the introductory section, §1, the basic definitions and known results are recalled for convenience of reference, and the main results are stated and proved in §2.
Convergence of cardinal series
Authors: de Boor Carl , Höllig Klaus , Riemenschneider Sherman
Published: June 2010

The result of this paper is a generalization of our characterization of the limits of multivariate cardinal splines. Let

M
n

{M_n}

denote the

n
n

-fold convolution of a compactly supported function

M
∈

L
2

(

R

d

)

M \in {L_2}({{\mathbf {R}}^d})

and denote by
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S Subscript n Baseline colon equals left-brace sigma-summation Underscript j element-of bold upper Z Superscript d Baseline Endscripts c left-parenthesis j right-parenthesis upper M Subscript n Baseline left-parenthesis dot negative j right-parenthesis colon c element-of l 2 left-parenthesis bold upper Z Superscript d Baseline right-parenthesis right-brace">

S
n

:=

{

∑

j
∈

Z

d

c
(
j
)

M
n

(
⋅
−
j
)
:
c
∈

l
2

(

Z

d

)

}

{S_n}: = \left \{ {\sum \limits _{j \in {{\mathbf {Z}}^d}} {c(j){M_n}( \cdot - j):c \in {l_2}({{\mathbf {Z}}^d})} } \right \}

\]
the span of the translates of

M
n

{M_n}

. We prove that there exists a set

Ω
\Omega

with

vol
d

(
Ω
)
=

(
2
π

)
d

{\operatorname {vol} _d}(\Omega ) = {(2\pi )^d}

such that for any

f
∈

L
2

(

R

d

)

f \in {L_2}({{\mathbf {R}}^d})

,
\[

dist
⁡
(
f
,

S
n

)
→
0

as 

n
→
∞
,

\operatorname {dist} (f,{S_n}) \to 0\quad {\text {as }}n \to \infty ,

\]
if and only if the support of the Fourier transform of

f
f

is contained in

Ω
\Omega

.
Pointwise estimates for convex polynomial approximation
Authors: Leviatan D.
Published: June 2010

For a convex function

f
∈
C
[
−
1
,
1
]

f \in C[ - 1,1]

we construct a sequence of convex polynomials

p
n

{p_n}

of degree not exceeding

n
n

such that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue f left-parenthesis x right-parenthesis equals p Subscript n Baseline left-parenthesis x right-parenthesis EndAbsoluteValue less-than-or-equal-to upper C omega 2 left-parenthesis f comma StartRoot 1 minus x squared EndRoot slash n right-parenthesis comma negative 1 less-than-or-equal-to x less-than-or-equal-to 1">

|

f
(
x
)
=

p
n

(
x
)

|

≤
C

ω
2

(
f
,

1
−

x
2

/

n
)
,
−
1
≤
x
≤
1

|f(x) = {p_n}(x)| \leq C{\omega _2}(f,\sqrt {1 - {x^2}} /n), - 1 \leq x \leq 1

. If in addition

f
f

is monotone it follows that the polynomials are also monotone thus providing simultaneous monotone and convex approximation.
A topological interpretation for the bias invariant
Authors: Dyer Micheal
Published: June 2010

The bias invariant has been used to distinguish between the homotopy types of

2
2

-complexes. In this note we show that two finite, connected

2
2

-complexes

X
X

and

Y
Y

with isomorphic fundamental groups and the same Euler characteristic have the same bias invariant if and only if there is a map

f
:
X
→
Y

f:X \to Y

which is a homology equivalence

π
1

f

{\pi _1}f

and

H
2

f

{H_2}f

are isomorphisms).
Toposes, monoid actions, and universal coalgebra
Authors: Davis Robert C.
Published: June 2010

A category cotripleable over Sets may be a topos, or may fail to be a topos in at least two distinct ways. One class of examples involves the category of

M
M

-sets and "strong" homomorphisms. For finite monoids

M
M

, this category is cotripleable iff the left ideals of

M
M

are totally ordered by inclusion.
The restricted tangent bundle of a rational curve on a quadric in 𝑃³
Authors: Ascenzi Maria-Grazia
Published: June 2010

Let

ψ
∗

T

P

3

{\psi ^*}{T_{{{\mathbf {P}}^3}}}

be the pull-back of the tangent bundle to

P

3

{{\mathbf {P}}^3}

via a parametrization

ψ
\psi

of a rational, reduced, irreducible curve

C
C

in

P

3

{{\mathbf {P}}^3}

contained in an irreducible quadric surface. Since

C
C

is rational, the bundle

ψ
∗

T

P

3

{\psi ^*}{T_{{{\mathbf {P}}^3}}}

splits into the direct sum of three line bundles. In this paper we study the relationship between the degrees of the line bundles of the splitting of

ψ
∗

T

P

3

{\psi ^*}{T_{{{\mathbf {P}}^3}}}

and the geometry of the curve

C
C

.
A lattice-theoretic equivalent of the invariant subspace problem
Authors: Longstaff W. E.
Published: June 2010

Every bounded linear operator on complex infinite-dimensional separable Hilbert space has a proper invariant subspace if and only if for every lattice automorphism

ϕ
\phi

of a certain abstract complete lattice

P
P

(defined by N. Zierler) there exists an element

a
∈
P

a \in P

different from 0 and 1 such that

ϕ
2

(
a
)
≤
a

{\phi ^2}(a) \leq a

.
Automatic continuity and openness of convex relations
Authors: Borwein J. M.
Published: June 2010

We establish open mapping and lower semicontinuity results for convex relations which are generalizations of classical results on continuity of positive linear mappings. These results do not require closure of the relation. Several applications are given.
Convolution estimates for some measures on curves
Authors: Oberlin Daniel M.
Published: June 2010

Suppose that

λ
\lambda

is a smooth measure on a curve in

R
3

{R^3}

. It is shown that

λ
∗

L
p

(

R
3

)
⊂

L
q

(

R
3

)

\lambda * {L^p}({R^3}) \subset {L^q}({R^3})

under certain conditions on

λ
,
p

\lambda ,p

and

q
q

.
On the cardinality of a compact 𝑇₁ space
Authors: Bella Angelo
Published: June 2010

In this paper two theorems on the cardinality of a compact

T
1

{T_1}

space are stated. They generalize the following result: an uncountable first countable compact

T
1

{T_1}

space has cardinality greater than or equal to

2

ℵ
0

{2^{{\aleph _0}}}

.
Orbits of creative subspaces
Authors: Downey R. G.
Published: June 2010

It is shown that the creative r.e. subspaces fall into infinitely many distinct elementary classes. The techniques also extend to give some new results about orbits of creative subspaces and subfields in

L
∗

(

V
∞

)

{L^*}({V_\infty })

and

L
∗

(

F
∞

)

{L^*}({F_\infty })

respectively. Finally within each of these new elementary classes we construct infinitely many further orbits in the automorphism group of

L
(

V
∞

)

L({V_\infty })

.
The existence of universal invariant semiregular measures on groups
Authors: Zakrzewski Piotr
Published: June 2010

A nonnegative, countably additive, extended real-valued measure is universal on a set

X
X

iff it is defined on all subsets of

X
X

, and is semiregular iff every set of positive measure contains a subset of positive finite measure. We prove that on every group of sufficiently large cardinality there exists a universal invariant semiregular measure vanishing on singletons. Thus we give complete solutions to the problems stated by Kannan and Raju [4] and Pelc [5].
Most normal operators are diagonal
Authors: Fong C. K.
Published: June 2010

We show that nondiagonal operators form a meager set in the set of all normal operators on a separable, infinite dimensional Hilbert space.
An equation alternately of retarded and advanced type
Authors: Cooke Kenneth L. , Wiener Joseph
Published: June 2010

We study a differential equation with the argument

2
[
(
t
+
1
)

/

2
]

2[(t + 1)/2]

, where

[
⋅
]

[ \cdot ]

denotes the greatest-integer function. The argument deviation

τ
(
t
)
=
t
−
2
[
(
t
+
1
)

/

2
]

\tau (t) = t - 2[(t + 1)/2]

is a function of period 2 and equals

t
t

for

−
1
⩽
t
>
1

- 1 \leqslant t > 1

. It changes its sign in each interval

2
n
−
1
⩽
t
>
2
n
+
1

2n - 1 \leqslant t > 2n + 1

.
A sampling theorem for analytic functions
Authors: Schiff J. L. , Walker W. J.
Published: June 2010

An analogue to the Shannon sampling theorem is obtained for an analytic function sampled on a circle.
Points de continuité d’une fonction séparément continue. II
Authors: Debs G.
Published: June 2010

We continue our previous investigations on the existence of joint continuity points for a separately continuous function defined on the product of a Baire space and a compact space.
The 𝐾-theory of triangular matrix rings. II
Authors: Keating M. E.
Published: June 2010

Let

T
T

be the upper triangular matrix ring defined by a pair of rings

R
R

and

S
S

and an

R
−
S

R - S

-bimodule

M
M

. We use the QP definition of algebraic

K
K

-theory to give a quick proof that the homomorphism
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi Subscript m Baseline colon upper K Subscript m Baseline left-parenthesis upper T right-parenthesis right-arrow upper K Subscript m Baseline left-parenthesis upper R right-parenthesis circled-plus upper K Subscript m Baseline left-parenthesis upper S right-parenthesis comma m greater-than-or-slanted-equals 0 comma">

π
m

:

K
m

(
T
)
→

K
m

(
R
)
⊕

K
m

(
S
)
,

m
⩾
0
,

{\pi _m}:{K_m}(T) \to {K_m}(R) \oplus {K_m}(S),\quad m \geqslant 0,

\]
induced by the obvious ring epimorphism is an isomorphism.
The corona theorem for domains whose boundary lies in a smooth curve
Authors: Moore Charles N.
Published: June 2010

We prove the corona theorem for domains whose boundary lies in a

C

1
+
α

{C^{1 + \alpha }}

curve.
Rational curve with one cusp. II
Authors: Yoshihara Hisao
Published: June 2010

Let

C
C

be a plane curve with

C
−
{
P
}
≅

A

1

C - \{ P\} \cong {{\mathbf {A}}^1}

for some point

P
∈
C

P \in C

and degree

d
≥
3

d \geq 3

. Let

{

e
1

,
…
,

e
t

}

\{ {e_1}, \ldots ,{e_t}\}

be the multiplicities of the infinitely near singular points of

P
P

. Then the following three conditions are equivalent: (1)

C
∖
L
≅

A

1

C\backslash L \cong {{\mathbf {A}}^1}

for some line

L
L

, (2)

d
=

e
1

+

e
2

(

in

case

t
=
1
,

let

e
2

=
1
)

d = {e_1} + {e_2}\, ({\text {in}}\;{\text {case}}\;t = 1,\;{\text {let}}\;{e_2} = 1)

, (3)

R
=

d
2

−

∑

i
=
1

t

e
i
2

−

e
t

+
1
≥
3

R = {d^2} - \sum \nolimits _{i = 1}^t {e_i^2 - {e_t} + 1 \geq 3}

.
An unconditional result about Grothendieck spaces
Authors: Haydon Richard
Published: June 2010

It is shown that if

X
X

is a nonreflexive Banach spach such that every weak* convergent sequence in

X
∗

{X^ * }

is also weakly convergent, then

X
∗

{X^ * }

has a subspace isometric to

L
1

(

{

0
,
1

}

ω
1

)

{L_1}({\left \{ {0,1} \right \}^{{\omega _1}}})
The noncompact hyperbolic 3-manifold of minimal volume
Authors: Adams Colin C.
Published: June 2010

We utilize maximal cusp volumes in order to prove that the Gieseking manifold is the unique complete noncompact hyperbolic

3
3

-manifold of minimal hyperbolic volume.
A note on the spherical maximal operator for radial functions
Authors: Leckband Mark
Published: June 2010

The spherical maximal operator for radial functions of

R

n

{{\mathbf {R}}^n}

is shown to be a restricted weak type

L
p

{L^p}

bounded operator for

p
=
n

/

(
n
−
1
)

p = n/(n - 1)

. The proof uses methods for restricted weak type single weight norm inequalities.
Quantum logics with lattice state spaces
Authors: Binder Jiří , Navara Mirko
Published: June 2010

LetLLbe a quantum logic and letS(L)S(L)denote the set of all states onLL. (By a state we mean a nonnegative boundedσ\sigma-additive measure, not necessarily normalized.) We ask whether every logic whose state space is a lattice has to be Boolean. We prove that this is so for finite logics and "projection logics." On the other hand, we show that there exist even concrete non-Boolean logics with a lattice state space (in fact, we prove that every countable concrete logic can be enlarged to a logic with a lattice state space). In the appendix we shortly consider the lattice properties of the set of observables and correct the paper [10].
Nonisoclinic 2-codimensional 4-webs of maximum 2-rank
Authors: Goldberg Vladislav V.
Published: June 2010

In recent papers, the author has proved that

4
4

-webs

W(4,2,2)

{\text {W(4,2,2)}}

of codimension 2 and maximum

2
2

-rank on a

4
4

-dimensional differentiable manifold are exceptional in the sense that they are not necessarily algebraizable, while maximum

2
2

-rank

2
2

-codimensional

d
d

-webs

W(d,2,2),

d
>
4

{\text {W(d,2,2),}}d > 4

, are algebraizable. Examples of exceptional isoclinic webs W(4,2, 2) were given in those papers. In the present paper, the author proves that a polynomial nonisoclinic

3
3

-web

W(3,2,2)

{\text {W(3,2,2)}}

cannot be extended to a nonisoclinic

4
4

-web

W(4,2,2)

{\text {W(4,2,2)}}

and constructs an example of a nonisoclinic

4
4

-web

W(4,2,2)

{\text {W(4,2,2)}}

of maximum

2
2

-rank.