bluuebunny/crossref_metadata_2025 huggingface dataset:
Grothendieck groups for hypersurface rings
Authors: Solberg Øyvind
Published: July 2010

Let

R
R

and

S
S

be commutative complete noetherian local Gorenstein domains. If the category of finitely generated maximal Cohen-Macaulay modules over

R
R

and

S
S

are stably equivalent and the equivalence commutes with the first syzygy functors, then we show that the Grothendieck groups for

R
R

and

S
S

are isomorphic. In particular, we apply this result to hypersurface rings.
A nonexistence result for Moore 𝐺-spectra
Authors: Costenoble S. R. , Waner S.
Published: July 2010

In this paper we show that certain equivariant Moore spectra do not exist. Specifically, we give an example of a Bredon coefficient system for which there is no corresponding equivariant Moore CW-spectrum that is bounded below. This nonexistence result is stronger than nonexistence results shown previously; nonexistence of an equivariant Moore spectrum of type

T
T

implies, in particular, that there are no equivariant Moore spaces of type

(
T
,
n
)

(T,n)

for any

n
n

. As a key step, we show that there is no strictly commutative Hopf space structure on the loop space

Q

S
0

Q{S^0}

agreeing up to infinite loop homotopy with the usual addition.
Nonexistence of almost complex structures on Grassmann manifolds
Authors: Sankaran Parameswaran
Published: July 2010

In this paper we prove that, for

3
≤
k
≤
n
−
3

3 \leq k \leq n - 3

, none of the oriented Grassmann manifolds,

G
~

n
,
k

{\widetilde {G}_{n,k}}

—except for

G
~

6
,
3

{\widetilde {G}_{6,3}}

, and a few as yet undecided cases—admits a weakly almost complex structure. The result for

k
=
1
,
2
,
n
−
1
,
n
−
2

k = 1,2,n - 1,n - 2

are well known and classical. The proofs make use of basic concepts in

K
K

-theory, the property that

G
~

n
,
k

{\widetilde {G}_{n,k}}

is

(
n
−
k
)

(n - k)

-universal, known facts about

K
(

H

P
4

)

K(\mathbb {H}{P^4})

, and characteristic classes.
An independence result in several complex variables
Authors: Lempert László , Rubel Lee A.
Published: July 2010

The assertion that there exists a complete set of biholomorphic invariants for simply connected domains in

C

2

{\mathbb {C}^2}

is proved to be independent of the axioms (ZFC) of set theory, give or take the Continuum Hypothesis.
A multivariate generalization of a theorem of R. H. Farrell
Authors: Plachky D.
Published: July 2010

Let

(
Ω
,

S

,
μ
)

(\Omega ,\mathfrak {S},\mu )

denote a finite measure space and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Subscript j Baseline colon normal upper Omega right-arrow left-bracket a Subscript j Baseline comma b Subscript j Baseline right-bracket left-parenthesis German upper S comma German upper B intersection left-bracket a Subscript j Baseline comma b Subscript j Baseline right-bracket right-parenthesis">

T
j

:
Ω
→
[

a
j

,

b
j

]
(

S

,

B

∩
[

a
j

,

b
j

]
)

{T_j}:\Omega \to [{a_j},{b_j}](\mathfrak {S},\mathfrak {B} \cap [{a_j},{b_j}])

-measurable functions,

j
=
1
,
…
,
n

j = 1, \ldots ,n

. Then the algebra of functions generated by

1
,

T
1

,
…
,

T
n

1,{T_1}, \ldots ,{T_n}

is a dense subset of

L

1

(
Ω
,

S

,
P
)

{\mathcal {L}_1}(\Omega ,\mathfrak {S},P)

if and only if for any

A
∈

S

A \in \mathfrak {S}

there exists some
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B element-of left-parenthesis upper T 1 comma ellipsis comma upper T Subscript n Baseline right-parenthesis Superscript negative 1 Baseline left-parenthesis German upper B Superscript n Baseline intersection left-bracket a 1 comma b 1 right-bracket times midline-horizontal-ellipsis times left-bracket a Subscript n Baseline comma b Subscript n Baseline right-bracket right-parenthesis">

B
∈

(

T
1

,
…
,

T
n

)

−
1

(

B

n

∩
[

a
1

,

b
1

]
×
⋯
×
[

a
n

,

b
n

]
)

B \in {({T_1}, \ldots ,{T_n})^{ - 1}}({\mathfrak {B}^n} \cap [{a_1},{b_1}] \times \cdots \times [{a_n},{b_n}])

, such that

μ
(
A
Δ
B
)
=
0

\mu (A\Delta B) = 0

is valid. In particular, this condition is satisfied if

(
Ω
,

S

)

(\Omega ,\mathfrak {S})

is a Blackwell space and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper T 1 comma ellipsis comma upper T Subscript n Baseline right-parenthesis colon normal upper Omega right-arrow left-bracket a 1 comma b 1 right-bracket times midline-horizontal-ellipsis times left-bracket a Subscript n Baseline comma b Subscript n Baseline right-bracket">

(

T
1

,
…
,

T
n

)
:
Ω
→
[

a
1

,

b
1

]
×
⋯
×
[

a
n

,

b
n

]

({T_1}, \ldots ,{T_n}):\Omega \to [{a_1},{b_1}] \times \cdots \times [{a_n},{b_n}]

is in addition one-to-one.
Distributive lattices having 𝑛-permutable congruences
Authors: Adams M. E. , Beazer R.
Published: July 2010

Distributive lattices having

n
n

-permutable congruences are characterized by the property that they have no

n
n

-element chain in their poset of prime ideals.
Weighted norm inequalities for operators of Hardy type
Authors: Bloom Steven , Kerman Ron
Published: July 2010

A new proof, yielding new conditions, is given for the two-weighted norm Hardy inequality. The theorem is extended to operators with kernels behaving much like the Riemann-Liouville fractional integrals of nonnegative order.
On the optimal asymptotic eigenvalue behaviour of weakly singular integral operators
Authors: Cobos Fernando , Janson Svante , Kühn Thomas
Published: July 2010

We improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.
Remarks on partitioner algebras
Authors: Dow Alan , Frankiewicz Ryszard
Published: July 2010

Partitioner algebras are defined in [1] and are a natural tool for studying the properties of maximal almost disjoint families of subsets of

ω
\omega

. We answer negatively two questions which were raised in [1]. We prove that there is a model in which the class of partitioner algebras is not closed under quotients and that it is consistent that there is a Boolean algebra of cardinality

ℵ
1

{\aleph _1}

which is not a partitioner algebra.
On fixed point theorems of nonexpansive mappings in product spaces
Authors: Tan Kok-Keong , Xu Hong Kun
Published: July 2010

We prove some fixed point theorems for nonexpansive self- and non-self-mappings in product spaces; in particular, we provide a constructive proof of a result of Kirk and Martinez and a partial answer to a question of Khamsi. Our proofs are elementary in the sense that we do not use any universal (or ultra) nets.
A Polish topology for the closed subsets of a Polish space
Authors: Beer Gerald
Published: July 2010

Let

⟨

X
,
d

⟩

\left \langle {X,d} \right \rangle

be a complete and separable metric space. The Wijsman topology on the nonempty closed subset

CL
⁡

(
X
)

\operatorname {CL}\left ( X \right )

of

X
X

is the weakest topology on

CL
⁡

(
X
)

\operatorname {CL}\left ( X \right )

such that for each

x
x

in

X
X

, the distance functional

A
→
d

(

x
,
A

)

A \to d\left ( {x,A} \right )

is continuous on

CL
⁡

(
X
)

\operatorname {CL}\left ( X \right )

. We show that this topology is Polish, and that the traditional extension of the topology to include the empty set among the closed sets is also Polish. We also compare the Borel class of a closed valued multifunction with its Borel class when viewed as a single-valued function into

CL
⁡

(
X
)

\operatorname {CL}\left ( X \right )

, equipped with Wijsman topology.
Discretization in the method of averaging
Authors: Fečkan Michal
Published: July 2010

Let

f
:
R
×

R

m
¯

×
R
→

R

m
¯

,
f
=
f
(
ε
,
x
,
t
)

f:R \times {R^{\overline m }} \times R \to {R^{\overline m }},f = f(\varepsilon ,x,t)

be a

C
2

{C^2}

-mapping

1
1

-periodic in

t
t

having the form

f
(
0
,
x
,
t
)
=
A
x
+
o
(

|

x

|

)

f(0,x,t) = Ax + o(|x|)

as

x
→
0

x \to 0

where

A
∈

L

(

R

m
¯

)

A \in \mathcal {L}({R^{\overline m }})

has no eigenvalues with zero real parts. We study the relation between local stable manifolds of the equation
\[

x
′

=
ε
f
(
ε
,
x
,
t
)
,
ε
>
0

is

small

x’ = \varepsilon f(\varepsilon ,x,t),\varepsilon > 0{\text {is}}\;{\text {small}}

\]
and of its discretization
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x Subscript n plus 1 Baseline equals x Subscript n Baseline plus left-parenthesis epsilon slash m right-parenthesis f left-parenthesis epsilon comma x Subscript n Baseline comma t Subscript n Baseline right-parenthesis comma t Subscript n plus 1 Baseline equals t Subscript n Baseline plus 1 slash m comma">

x

n
+
1

=

x
n

+
(
ε

/

m
)
f
(
ε
,

x
n

,

t
n

)
,

t

n
+
1

=

t
n

+
1

/

m
,

{x_{n + 1}} = {x_n} + (\varepsilon /m)f(\varepsilon ,{x_n},{t_n}),{t_{n + 1}} = {t_n} + 1/m,

\]
where

m
∈
{
1
,
2
,
…
}
=

N

m \in \{ 1,2, \ldots \} = \mathcal {N}

. We show behavior of these manifolds of the discretization for the following cases: (a)

m
→
∞
,
ε
→

ε
¯

>
0

m \to \infty ,\varepsilon \to \overline \varepsilon > 0

, (b)

m
→
∞
,
ε
→
0

m \to \infty ,\varepsilon \to 0

, (c)

m
→
k
∈

N

,
ε
→
0

m \to k \in \mathcal {N},\varepsilon \to 0

.
On weak reverse integral inequalities for mean oscillations
Authors: Franciosi Michelangelo
Published: July 2010

We prove that if

f
f

verifies a reverse Hölder inequality with exponent

p
,
1
>
p
>
+
∞

p,1 > p > + \infty

, then

(
M
f
+

f
#

)
p

{(Mf + {f^\# })^p}

is a

A
1

{A_1}

-weight of Muckenhoupt, where

M
f

Mf

is the Hardy-Littlewood maximal function and

f
#

{f^\# }

the Fefferman-Stein maximal function.
Estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup
Authors: Gutiérrez Cristian E. , Urbina Wilfredo O.
Published: July 2010

We show pointwise estimates for the maximal operator of the Ornstein-Uhlenbeck semigroup for functions that are integrable with respect to the Gaussian measure. The estimates are used to prove pointwise convergence.
The monodromy of certain families of linear series is at least the alternating group
Authors: Edidin Dan
Published: July 2010

Let

g
,
r
,
d

g,r,d

be positive integers such that the Brill-Noether number,

ρ
(
g
,
r
,
d
)
:=
g
−
(
r
+
1
)
(
g
−
d
+
r
)
=
0

\rho (g,r,d): = g - (r + 1)(g - d + r) = 0

. We prove that if

r
+
1
≠
g
−
d
+
r

r + 1 \ne g - d + r

, then for suitable families of curves

(
C

/

B
)

(C/B)

, the monodromy of the family

G
d
r

(
C

/

B
)
→
B

G_d^r(C/B) \to B

is at least the alternating group. Our techniques are combinatorial, and similar to those used by Bercov and Proctor in their paper [BP].
Weak compactness in 𝐿¹(𝜇,𝑋)
Authors: Ülger A.
Published: July 2010

Let

(
Ω
,
Σ
,
μ
)

(\Omega ,\Sigma ,\mu )

be a probability space,

X
X

a Banach space, and

L
1

(
μ
,
X
)

{L^1}(\mu ,X)

the Banach space of Bochner integrable functions

f
:
Ω
→
X

f:\Omega \to X

. Let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper W equals left-brace f element-of upper L Superscript 1 Baseline left-parenthesis mu comma upper X right-parenthesis colon for a period e period omega in normal upper Omega comma StartAbsoluteValue EndAbsoluteValue f left-parenthesis omega right-parenthesis StartAbsoluteValue EndAbsoluteValue less-than-or-equal-to 1 right-brace">

W
=
{
f
∈

L
1

(
μ
,
X
)
:

 for a

.e

. 

ω

 in 

Ω
,

|

|

f
(
ω
)

|

|

≤
1
}

W = \{ f \in {L^1}(\mu ,X):{\text { for a}}{\text {.e}}{\text {. }}\omega {\text { in }}\Omega ,||f(\omega )|| \leq 1\}

. In this paper we characterize the rwc (relatively weakly compact) subsets of

L
1

(
μ
,
X
)

{L^1}(\mu ,X)

. The main results are as follows: Theorem A. A subset

H
H

of

W
W

is rwc iff given any sequence

(

f
n

)

({f_n})

in

H
H

there exists a sequence

(

f
~

n

)

({\tilde f_n})

, with

f
~

n

∈
Co
⁡
(

f
n

,

f

n
+
1

,
…
)

{\tilde f_n} \in \operatorname {Co}({f_n},{f_{n + 1}}, \ldots )

such that, for a.e.

ω
\omega

in

Ω
\Omega

, the sequence

(

f
~

n

(
ω
)
)

({\tilde f_n}(\omega ))

converges weakly in

X
X

. Theorem B. A subset

A
A

of

L
1

(
μ
,
X
)

{L^1}(\mu ,X)

is rwc iff given any

ε
>
0

\varepsilon > 0

there exist an integer

N
N

and a rwc subset

H
H

of NW such that

A
⊆
H
+
ε
B
(
0
)

A \subseteq H + \varepsilon B(0)

, where

B
(
0
)

B(0)

is the unit ball of

L
1

(
μ
,
X
)

{L^1}(\mu ,X)

.
Polynomials with nonnegative coefficients
Authors: Barnard R. W. , Dayawansa W. , Pearce K. , Weinberg D.
Published: July 2010

The authors verify the conjecture that a conjugate pair of zeros can be factored from a polynomial with nonnegative coefficients so that the resulting polynomial still has nonnegative coefficients. The conjecture was originally posed by A. Rigler, S. Trimble, and R. Varga arising out of their work on the Beauzamy-Enflo generalization of Jensen’s inequality. The conjecture was also made independently by B. Conroy in connection with his work in number theory. A crucial and interesting lemma is proved which describes general coefficient-root relations for polynomials with nonnegative coefficients and for polynomials for which the case of equality holds in Descarte’s Rule of Signs.
The Euclidean factor of a Hadamard manifold
Authors: Adachi Toshiaki , Ohtsuka Fumiko
Published: July 2010

The ideal boundary

X
(
∞
)

X(\infty )

of a Hadamard manifold

X
X

is the set of asymptotic classes of rays on

X
X

. We shall characterize the Euclidean factor of

X
X

by information on

X
(
∞
)

X(\infty )

. Under the assumption that the diameter of

X
(
∞
)

X(\infty )

is

π
\pi

, we call a boundary point that has a unique point of Tits distance

π
\pi

a polar point. We shall show that such points form a standard sphere and compose the boundary of the Euclidean factor of the given Hadamard manifold.
Hermitian surfaces and a twistor space of algebraic dimension 2
Authors: Pontecorvo Massimiliano
Published: July 2010

We study anti-self-dual hermitian surfaces with odd first Betti number. We show that the twistor space of a Hopf surface

M
M

has algebraic dimension 2, and we prove existence of half-conformally-flat metrics on the connected sum of copies of

M
M

and

C

P

2

\mathbb {C}{\mathbb {P}_2}

. Finally we emphasize some differences with the case

b
1

{b_1}

even.
A rigid Borel space
Authors: Aniszczyk Bohdan
Published: July 2010

We construct a rigid

σ
\sigma

-algebra on a set of cardinality

ω
1

{\omega _1}

.
Real zeros of random algebraic polynomials
Authors: Farahmand K.
Published: July 2010

There are many known asymptotic estimates of the expected number of real zeros of algebraic polynomials with independent random coefficients of equal means. The present paper considers the case when the means of the coefficients are not all necessarily equal. The expected number of crossings of two algebraic polynomials with unequal degree flows from the results.
Linking and the shadowing property for piecewise monotone maps
Authors: Chen Liang
Published: July 2010

A necessary and sufficient condition for a continuous uniformly piecewise linear map of a compact interval to have the Shadowing Property is that its turning point set be linked.
Two-bridge links with unlinking number one
Authors: Kohn Peter
Published: July 2010

Three conditions equivalent to a two-bridge link having unlinking number one are given. As a corollary it is shown that an unknotting crossing appears in the minimal diagram of a two-bridge knot or link. In addition, the absolute value of the linking number of the components is computed for all unlinking number one two-bridge links.
Spaces without cohomological dimension preserving compactifications
Authors: Dydak Jerzy , Walsh John J.
Published: July 2010

Examples are constructed that include: first, a separable metric space having cohomological dimension 4 such that every Hausdorff compactification has cohomological dimension at least 5; second, a locally compact metric space having cohomological dimension 4 whose Stone-Čech compactification has infinite cohomological dimension.
Maximal ideals in Laurent polynomial rings
Authors: Nashier Budh
Published: July 2010

We prove, among other results, that the one-dimensional local domain

A
A

is Henselian if and only if for every maximal ideal

M
M

in the Laurent polynomial ring

A
[
T
,

T

−
1

]

A[T,{T^{ - 1}}]

, either

M
∩
A
[
T
]

M \cap A[T]

or

M
∩
A
[

T

−
1

]

M \cap A[{T^{ - 1}}]

is a maximal ideal. The discrete valuation ring

A
A

is Henselian if and only if every pseudoWeierstrass polynomial in

A
[
T
]

A[T]

is Weierstrass. We apply our results to the complete intersection problem for maximal ideals in regular Laurent polynomial rings.
The class of all 𝑆-pregroups is not finitely axiomatizable
Authors: Dekov Deko V.
Published: July 2010

In order to investigate the amalgamated free products of groups, in 1950 R. Baer (Free sums of groups and their generalizations. II, Amer. J. Math. 72 (1950), 625-646) introduced the concept of an

S
S

-pregroup and gave an infinite set of elementary (i.e., of a first-order language) axioms for

S
S

-pregroups. The term "

S
S

-pregroup" was introduced by J. R. Stallings (Adian groups and pregroups, Essays in Group Theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer-Verlag, New York, 1987, pp. 321-342), who suggested the problem of finding a finite set of elementary axioms for

S
S

-pregroups (ibid, Question 5, The first part, p. 340). In the present paper we show that the class of all

S
S

-pregroups is not finitely axiomatizable, i.e., it cannot be characterized by any finite set of elementary axioms.
A short proof of the Y. Katznelson’s and L. Tzafriri’s theorem
Authors: Phóng Vũ Quôc
Published: July 2010

A short proof is given to the following theorem of Y. Katznelson and L. Tzafriri: Let

T
T

be a power-bounded operator in a Banach space

E
E

. Then

lim

n
→
∞

|

|

T

n
+
1

−

T
n

|

|

=
0

{\lim _{n \to \infty }}||{T^{n + 1}} - {T^n}|| = 0

if and only if

σ
(
T
)
∩
{
z
∈

C

:

|

z

|

=
1
}
⊂
{
1
}

\sigma (T) \cap \{ z \in \mathbb {C}:|z| = 1\} \subset \{ 1\}

.
The Evans-Griffith syzygy theorem and Bass numbers
Authors: Bruns Winfried
Published: July 2010

Let

(
R
,

m

)

(R,\mathfrak {m})

be a Noetherian local ring containing a field. The syzygy theorem of Evans and Griffith (see The syzygy problem, Ann. of Math. (2) 114 (1981), 323-353) says that a nonfree

m
m

th syzygy module

M
M

over

R
R

which has finite projective dimension must have rank

≥
m

\geq m

. This theorem is an assertion about the ranks of the homomorphisms in certain acyclic complexes. It is the aim of this paper to demonstrate that the condition of acyclicity can be relaxed in a natural way. We shall use the generalization thus obtained to show that the Bass numbers of a module satisfy restrictions analogous to those which the syzygy theorem imposes on Betti numbers.
Density of the polynomials in the Hardy space of certain slit domains
Authors: Akeroyd John
Published: July 2010

In this article we construct a Jordan arc

Γ
\Gamma

in the complex plane, with endpoints 0 and 1, such that the polynomials are dense in the Hardy space
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H squared left-parenthesis double-struck upper D slash normal upper Gamma right-parenthesis semicolon double-struck upper D colon equals StartSet z element-of double-struck upper C colon StartAbsoluteValue z EndAbsoluteValue greater-than 1 EndSet">

H
2

(

D

/

Γ
)
;

D

:=
{
z
∈

C

:

|

z

|

>
1
}

{H^2}(\mathbb {D}/\Gamma );\mathbb {D}: = \{ z \in \mathbb {C}:|z| > 1\}

.
The behavior of the analytically continued resolvent operator near 𝜅=0 and an application to energy decay
Authors: Yamamoto Kazuhiro
Published: July 2010

We shall study the behavior of the analytically continued resolvent operator

R
+

(
κ
)

{R^ + }(\kappa )

for perturbations of

−
Δ

- \Delta

in a neighborhood of

κ
=
0

\kappa = 0

. As an application, making use of Vainberg’s argument, we shall show the local energy decay of solutions to generalized wave equations whose stationary problems are not positive definite.
A note on a theorem of J. Diestel and B. Faires
Authors: Ferrando J. C. , López Pellicer M.
Published: July 2010

Applying a property concerning certain coverings of

l
0
∞

(
X
,

A

)

l_0^\infty (X,\mathcal {A})

that always contain some elements that are barrelled and dense in

l
0
∞

(
X
,

A

)

l_0^\infty (X,\mathcal {A})

, we generalize a localization theorem of M. Valdivia, relative to vector bounded finitely additive measures (Theorem 1), and obtain two different generalizations of a theorem of J. Diestel and B. Faires ensuring that certain finitely additive measures are countably additive (Theorems 2 and 3). The original proof of the quoted theorem of Diestel and Faires uses a theorem of Rosenthal that is not required in our proof of Theorem 3. This avoids imposing over the Valdivia’s

Λ
r

{\Lambda _r}

-spaces defining the measure range space, the condition that they do not contain a copy of

l
∞

{l^\infty }

.
Positivity of global branches of fully nonlinear elliptic boundary value problems
Authors: Healey Timothy J. , Kielhöfer Hansjörg
Published: July 2010

We consider a bifurcation problem for a general class of fully nonlinear, second-order elliptic equations on a regular bounded domain in

R

n

{\mathbb {R}^n}

and subject to homogeneous Dirichlet boundary data. We assume that the linearized problem about the trivial solution possesses a positive solution for at least one isolated parameter value. With no other growth or sign conditions imposed upon the nonlinearity, we establish the existence of a global branch of nontrivial positive solutions. Moreover, if there is only one such isolated value of the parameter, we deduce that the branch of positive solutions is unbounded.
Lipscomb’s 𝐿(𝐴) space fractalized in Hilbert’s 𝑙²(𝐴) space
Authors: Lipscomb S. L. , Perry J. C.
Published: July 2010

By extending adjacent-endpoint identification in Cantor’s space

N
(
{
0
,
1
}
)

N(\{ 0,1\} )

to Baire’s space

N
(
A
)

N(A)

, we move from the unit interval

I
=
L
(
{
0
,
1
}
)

I = L(\{ 0,1\} )

to

L
(
A
)

L(A)

. The metric spaces

L

(
A

)

n
+
1

L{(A)^{n + 1}}

and

L

(
A

)
∞

L{(A)^\infty }

have provided nonseparable analogues of Nöbeling’s and Urysohn’s imbedding theorems. To date, however,

L
(
A
)

L(A)

has no metric description. Here, we imbed

L
(
A
)

L(A)

in

l
2

(
A
)

{l^2}(A)

and the induced metric yields a geometrical interpretation of

L
(
A
)

L(A)

. Except for the small last section, we are concerned with the imbedding. Once inside

l
2

(
A
)

{l^2}(A)

, we see

L
(
A
)

L(A)

as a subspace of a "closed simplex"

Δ
A

{\Delta ^A}

having the standard basis vectors together with the origin as vertices. The part of

L
(
A
)

L(A)

in each

n
n

-dimensional face

σ
n

{\sigma ^n}

of

Δ
A

{\Delta ^A}

is a "generalized Sierpiński Triangle" called an

n
n

-web

ω
n

{\omega ^n}

. Topologically,

ω
n

{\omega ^n}

is

L
(
{
0
,
1
,
…
,
n
}
)

L(\{ 0,1, \ldots ,n\} )

. For

n
=
2
,

ω
2

n = 2,{\omega ^2}

is just the usual Sierpiński Triangle in

E
2

{E^2}

; for

n
=
3
,

ω
3

n = 3,{\omega ^3}

is Mandelbrot’s fractal skewed web. Thus,

L
(
A
)
→

l
2

(
A
)

L(A) \to {l^2}(A)

invites an extension of fractals. That is, when

|

A

|

|A|

infinite, Baire’s Space

N
(
A
)

N(A)

is a "generalized code space" on

|

A

|

|A|

symbols that addresses the points of the "generalized fractal"

L
(
A
)

L(A)

.
Weinbaum’s conjecture on unique subwords of nonperiodic words
Authors: Duncan Andrew J. , Howie James
Published: July 2010

Following a conjecture of Weinbaum, we show that every nonperiodic word

W
W

of length at least 2 in a free group has a cyclic permutation of the form UV, where each of

U
U

and

V
V

occur precisely once as a cyclic subword of

W
W

and neither occurs as a cyclic subword of

W

−
1

{W^{ - 1}}

. In fact, we prove a somewhat stronger version of this result and also give a number of applications to one-relator products of groups.
Handlebody complements in the 3-sphere: a remark on a theorem of Fox
Authors: Scharlemann Martin
Published: July 2010

Let

W
W

be a compact

3
3

-dimensional submanifold of

S
3

{S^3}

, and

C
C

be a collection of disjoint simple closed curves on

∂
W

\partial W

. We give necessary and sufficient conditions (one extrinsic, one intrinsic) for

W
W

to have an imbedding in

S
3

{S^3}

so that

S
3

−
W

{S^3} - W

is a union of handlebodies, and

C
C

contains a complete collection of meridia for these handlebodies.
Two weight norm inequalities for fractional one-sided maximal operators
Authors: Martín-Reyes F. J. , de la Torre A.
Published: July 2010

In this paper we introduce a new maximal function, the dyadic one-sided maximal function. We prove that this maximal function is equivalent to the one-sided maximal function studied by the authors and Ortega in Weighted inequalities for one-sided maximal functions (Trans. Amer. Math. Soc. 319 (1990)) and by Sawyer in Weighted inequalities for the one-sided Hardy-Littlewood maximal functions (Trans. Amer. Math. Soc. 297 (1986)), but our function, being dyadic, is much easier to deal with, and it allows us to study fractional maximal operators. In this way we obtain a geometric proof of the characterization of the good weights for fractional maximal operators, answering a question raised by Andersen and Sawyer in Weighted norm inequalities for the Riemann-Liouville and Weyl fractional integral operators (Trans. Amer. Math. Soc. 308 (1988)). Our methods, avoiding complex interpolation, give also the case of different weights for the fractional maximal operator, which was an open problem.
Extrinsic upper bounds for eigenvalues of Dirac-type operators
Authors: Anghel N.
Published: July 2010

Extrinsic estimates from above for eigenvalues of generalized Dirac operators on compact manifolds are given. They depend on the second fundamental form of any isometric immersion of the manifold in some Euclidean space and the curvature term in the Bochner-Weitzenböck formula for the square of the Dirac operator. Most of the known extrinsic upper bounds for the first eigenvalue of the Laplacian are in this way easily recovered and extended.
The subalgebra of 𝐿¹(𝐴𝑁) generated by the Laplacian
Authors: Hebisch Waldemar
Published: July 2010

We prove that for the Iwasawa

A
N

AN

groups corresponding to complex semisimple Lie groups, the subalgebra of

L
1

(
A
N
)

{L^1}(AN)

associated to a distinguished laplacian is isomorphic with the algebra of integrable radial functions on

R
n

{R^n}

.
Un phénomène d’explosion du spectre
Authors: Houimdi M.
Published: July 2010

Dans cet article on donne un exemple d’opérateur shift à poids quasinilpotent, tel que l’algébre fermée pour la topologie faible des opérateurs, engendrée par ce shift, contient un élément dont le spectre non réduit à un point. Cet exemple constitue une réponse affirmative à la question

6
6

soulevée par A. L. Shields dans Weighted shift operators and analytic function theory, Topics in Operator Theory (C. Pearcy, ed.), Math. Surveys Monographs, vol. 13, Amer. Math. Soc., Providence, RI, 1974, pp. 49-128.
Asymptotic behavior of almost-orbits of nonlinear semigroups of non-Lipschitzian mappings in Hilbert spaces
Authors: Tan Kok-Keong , Xu Hong Kun
Published: July 2010

Let

C
C

be a nonempty closed convex subset of a Hilbert space

H
H

,

F

=
{
T
(
t
)
:
t
⩾
0
}

\mathcal {F} = \{ T(t):t \geqslant 0\}

be a continuous nonlinear asymptotically nonexpansive semigroup acting on

C
C

with a nonempty fixed point set

F
(

F

)

F(\mathcal {F})

, and

u
:
[
0
,
∞
)
→
C

u:[0,\infty ) \to C

be an almost-orbit of

F

\mathcal {F}

. Then

{
u
(
t
)
}

\{ u(t)\}

almost converges weakly to a fixed point of

F

\mathcal {F}

, i.e., there exists an element

y
y

in

F
(

F

)

F(\mathcal {F})

such that
\[

weak-

lim

1
t

∫
0
t

u
(
r
+
h
)
d
r
=
y

uniformly for 

h
⩾
0.

{\text {weak-}}\lim \frac {1} {t}\int _0^t {u(r + h)dr = y\quad {\text {uniformly for }}h \geqslant 0.}

\]
This implies that

{
u
(
t
)
}

\{ u(t)\}

converges weakly to a fixed point of

F

\mathcal {F}

if and only if

{
u
(
t
+
h
)
−
u
(
t
)
}

\{ u(t + h) - u(t)\}

converges weakly to zero as

t
t

tends to infinity for each

h
⩾
0

h \geqslant 0

.
The boundedly controlled Whitehead theorem
Authors: Anderson Douglas R. , Munkholm Hans Jørgen
Published: July 2010

This note contains a version of the Whitehead Theorem for boundedly controlled maps of CW complexes that is often useful in applications and complements the Whitehead Theorem in our book Boundedly controlled topology (Lecture Notes in Math., vol. 1323, Springer-Verlag, 1988). We also include a version of the Whitehead Theorem valid for simply connected boundedly controlled CW complexes.
Periodic 𝐿²-solutions of an integrodifferential equation in a Hilbert space
Authors: Staffans Olof J.
Published: July 2010

Let

A
A

be a closed, densely defined operator in a Hilbert space

X
X

, and let

μ
,

ν

\mu ,\;\nu

, and

η
\eta

be finite, scalar-valued measures on

R

{\mathbf {R}}

. Consider the abstract integrodifferential equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Underscript bold upper R Endscripts StartFraction d Over d t EndFraction u left-parenthesis t minus s right-parenthesis mu left-parenthesis d s right-parenthesis plus integral Underscript bold upper R Endscripts u left-parenthesis t minus s right-parenthesis nu left-parenthesis d s right-parenthesis plus integral Underscript bold upper R Endscripts upper A u left-parenthesis t minus s right-parenthesis eta left-parenthesis d s right-parenthesis equals f left-parenthesis t right-parenthesis comma t element-of bold upper R comma">

∫

R

d

d
t

u
(
t
−
s
)
μ
(
d
s
)
+

∫

R

u
(
t
−
s
)
ν
(
d
s
)
+

∫

R

A
u
(
t
−
s
)
η
(
d
s
)
=
f
(
t
)
,

t
∈

R

,

\int _{\mathbf {R}} {\frac {d} {{dt}}u(t - s)\mu (ds) + \int _{\mathbf {R}} {u(t - s)\nu (ds) + \int _{\mathbf {R}} {Au(t - s)\eta (ds) = f(t),\qquad t \in {\mathbf {R}},} } }

\]
where

f
f

is a

2
π

2\pi

-periodic

L
2

{L^2}

function with values in

X
X

. We give necessary and sufficient conditions for this equation to have a mild

2
π

2\pi

-periodic

L
2

{L^2}

-solution with values in

X
X

for all

f
f

, as well as necessary and sufficient conditions for it to have a strong solution for all

f
f

. Furthermore, we give necessary and sufficient conditions for the operator mapping

f
f

into the periodic solution

u
u

to be compact. These results are applied to prove existence of periodic solutions of a nonlinear equation.
The ideal determined by the unsymmetric game
Authors: Newelski L. , Rosłanowski A.
Published: July 2010

In the present paper we study the ideal of all subsets of

X

ω

{\mathcal {X}^\omega }

for which the second player has a winning strategy in the unsymmetric game. We describe its cardinal coefficients and the notions of forcing determined by it.
Finite substructure lattices of models of Peano arithmetic
Authors: Schmerl James H.
Published: July 2010

Some new finite lattices (for example,

M
4

,

M
7

{M_4},\;{M_7}

, and the hexagon lattice) are shown to be isomorphic to the lattice of elementary substructures of a model of Peano Arithmetic.
A sufficient arithmetical condition for the ideal class group of an imaginary quadratic field to be cyclic
Authors: Ishibashi Mākoto
Published: July 2010

We give a sufficient arithmetical condition for the ideal class group of an imaginary quadratic field to be cyclic by using Ono’s number.
Uniqueness and stability of nonnegative solutions for semipositone problems in a ball
Authors: Ali Ismael , Castro Alfonso , Shivaji R.
Published: July 2010

We study the uniqueness and stability of nonnegative solutions for classes of nonlinear elliptic Dirichlet problems on a ball, when the nonlinearity is monotone, negative at the origin, and either concave or convex.
Initial values of solutions of the Navier-Stokes equations
Authors: Calderón Calixto P.
Published: July 2010

This paper considers weak solutions to the Navier-Stokes equations in the sense considered in previous papers of the author and of Fabes, Jones, and Rivière. Results concerning pointwise a.e. convergence of the solutions to the initial values are established. The initial values that are considered here are divergence free vector functions belonging to

L
p

(

R
n

)

{L^p}({R^n})

, for

p
p

greater than or equal to the dimension

n
n

.
Integral representations for Riesz systems in the unit ball and some applications
Authors: Djrbashian Ashot
Published: July 2010

We introduce

A
α
p

A_\alpha ^p

spaces of systems of harmonic functions satisfying Cauchy-Riemann equations in

R

n

{{\mathbf {R}}^{\mathbf {n}}}

and find integral representations. Using these representations and estimates for the integral kernel we prove boundedness of the representation operator in

L
p

{L^p}

and Lipschitz classes.
The time spent by the Wiener process in a narrow tube before leaving a wide tube
Authors: Földes Antónia , Puri Madan L.
Published: July 2010

The almost sure behavior of the time spent by the Wiener process in a "small interval" before first leaving a "bigger interval" is investigated.
A proof of new summation formulae by using sampling theorems
Authors: Zayed Ahmed I.
Published: July 2010

Using symbolic manipulation programs, William Gosper has obtained in the last two years new, but unusual, summation formulae involving trigonometric functions. Recently, Ismail and Zhang have been able to prove mathematically some of these formulae and generalize them to summation formulae involving the Bessel functions of the first kind. In this paper we show that some of Gosper’s formulae, as well as their generalization by Ismail and Zhang, can be obtained from already known results in sampling theory. Moreover, we show that sampling theory can actually produce other new summation formulae, involving different kinds of special functions, in a straightforward fashion.
A sharp estimate for 𝐴^{𝑝}_{𝛼} functions in 𝐶ⁿ
Authors: Vukotić Dragan
Published: July 2010

We observe that involutive automorphisms

φ
a

{\varphi _a}

of the unit ball in

C

n

{{\mathbf {C}}^n}

induce surjective involutive isometries of the weighted Bergman space

A
α
p

(
0
>
p
>
∞
,

α
>
−
1
)

A_\alpha ^p(0 > p > \infty ,\;\alpha > - 1)

. By means of these isometries we solve an extremal problem for the point-evaluation functional, thus obtaining a sharp estimate for

|

f
(
z
)

|

|f(z)|

in terms of

|

|

f

|

|

p
,
α

||f|{|_{p,\alpha }}

and

|

z

|

|z|

.
Toeplitz operators on Cartan domains essentially commute with a bilateral shift
Authors: Engliš Miroslav
Published: July 2010

For bounded symmetric domains

Ω
⊂

C

N

\Omega \subset {{\mathbf {C}}^N}

, a bilaterial shift operator

U
U

is shown to exist on the Bergman space

A
2

(
Ω
)

{A^2}(\Omega )

such that

U

T
f

−

T
f

U

U{T_f} - {T_f}U

is a compact operator for all Toeplitz operators

T
f

{T_f}

. This may be viewed as an extension of the well-known fact that

S

∗

T
S
−
T
=
0

{S^{\ast }}TS - T = 0

whenever

T
T

is a Toeplitz operator on

H
2

,

S

{H^2},\;S

being the unilateral shift. It also follows that the

C

∗

{C^{\ast }}

-algebra generated by Toeplitz operators on

A
2

(
Ω
)

{A^2}(\Omega )

does not contain all bounded operators.
Pointwise multipliers of weighted BMO spaces
Authors: Yabuta Kôzô
Published: July 2010

In a recent paper by S. Bloom (Pointwise multipliers of weighted

B
M
O

BMO

spaces, Proc. Amer. Math. Soc. 105 (1989), 950-960), there are some inaccuracies. In this note, we give a counterexample to his "theorem" and a corrected form with proof under a suitable condition on weights. We also give some remarks and examples.
Short chains and regular components
Authors: Reiten Idun , Skowroński Andrzej , Smalø Sverre O.
Published: July 2010

Let

Λ
\Lambda

be a finite-dimensional

k
k

-algebra with

k
k

an algebraically closed field and

ind
⁡
Λ

\operatorname {ind} \Lambda

a chosen subcategory of a complete set of isomorphism classes of finitely generated indecomposable

Λ
\Lambda

-modules. This paper deals with the regular components of

ind
⁡
Λ

\operatorname {ind} \Lambda

consisting of modules that are not the middle of any short chain. It is proved that the number of such components containing only a finite number of

D
T
r

DTr

-orbits is finite. Further, the infinite radical of such a component is zero and the component is isomorphic to the mesh category of its underlying translation quiver. Families of selfinjective algebras having such components are constructed.
A characterization of hyperbolic manifolds
Authors: Abate Marco
Published: July 2010

In this note we prove that a complex manifold

X
X

is Kobayashi hyperbolic if and only if the space

Hol
⁡
(
Δ
,
X
)

\operatorname {Hol} (\Delta ,X)

of holomorphic maps of the unit disk

Δ
\Delta

into

X
X

is relatively compact (with respect to the compact-open topology) in the space

C
(
Δ
,

X

∗

)

C(\Delta ,{X^{\ast }})

of continuous maps from

Δ
\Delta

into the one-point compactification

X

∗

{X^{\ast }}

of

X
X

.
A characterization of abelian groups
Authors: Brailovsky L.
Published: July 2010

Let

G
G

be a group and let

k
>
2

k > 2

be an integer such that

(

k
3

−
k
)
>

|

G

|

/

2

({k^3} - k) > |G|/2

if

G
G

is finite. Suppose that the condition

|

A
2

|

⩽
k
(
k
+
1
)

/

2

|{A^2}| \leqslant k(k + 1)/2

is satisfied by every

k
k

-element subset

A
⊆
G

A \subseteq G

. Then

G
G

is abelian.
Representing positive homology classes of 𝐶𝑃²#2\overline{𝐶𝑃}² and 𝐶𝑃²#3\overline{𝐶𝑃}²
Authors: Kikuchi Kazunori
Published: July 2010

Theorems of Donaldson are used to give a necessary and sufficient condition for a given second integral homology class

ξ
\xi

of

C

P
2

#
n

C

P

¯

2

{\mathbf {C}}{P^2}\# n{\overline {{\mathbf {C}}P} ^2}

to be represented by a smoothly embedded

2
2

-sphere (1) for

n
=
2
,

3

n = 2,\;3

and

ξ
\xi

positive (with self-intersection positive), and (2) for

n
=
3

n = 3

and

ξ
\xi

characteristic. Case (2) is a consequence of a more general result on the characteristic embedding of

2
2

-spheres into

4
4

-manifolds, which result generalizes the theorem of Donaldson on spin

4
4

-manifolds just as the result of Kervaire and Milnor on the characteristic embedding extends Rohlin’s signature theorem.
Discretization of second-order variational systems
Authors: Fečkan Michal
Published: July 2010

The existence of periodic orbits of the discretization of second-order variational systems is studied both for varying step of discretization and for a fixed small one.
Two theorems of Josefson-Nissenzweig type for Fréchet spaces
Authors: Bonet J. , Lindström M. , Valdivia M.
Published: July 2010

We characterize the Fréchet-Montel (respectively, Fréchet-Schwartz) spaces by sequences in their dual spaces.
The full group of a countable measurable equivalence relation
Authors: Mercer Richard
Published: July 2010

We study the group of all "

R
R

-automorphisms" of a countable equivalence relation

R
R

on a standard Borel space, special Borel automorphisms whose graphs lie in

R
R

. We show that such a group always contains periodic maps of each order sufficient to generate

R
R

. A construction based on these periodic maps leads to totally nonperiodic

R
R

-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for

R
R

-automorphisms. Finally we show that this group always contains copies of free groups on any countable number of generators.
Weighted Sobolev inequalities on domains satisfying the chain condition
Authors: Chua Seng-Kee
Published: July 2010

By similar methods of Iwaniec and Nolder (Hardy-Littlewood inequality for quasiregular mappings in certain domains in

R

n

{\mathbb {R}^n}

, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985)), we obtain weighted Sobolev inequalities on domains satisfying the Boman chain condition.
On quantum spaces of Lie algebras
Authors: Le Bruyn Lieven , Van den Bergh Michel
Published: July 2010

The homogenization

H
(

g

)

H(\mathfrak {g})

of the enveloping algebra of a finite dimensional Lie algebra

g

\mathfrak {g}

is an Artin-Schelter regular algebra. We characterize

d
d

-dimensional linear subspaces in the corresponding quantum space

P

q

(

g

)

{\mathbb {P}_q}(\mathfrak {g})

as homogenizations of induced representations from codimension

d
d

Lie subalgebras. Furthermore we prove that the point variety has an embedded component iff there is a line, not contained in this point variety.
Differentiability of the norm in von Neumann algebras
Authors: Taylor Keith F. , Werner Wend
Published: July 2010

Smooth points in von Neumann algebras are characterized in terms of minimal projections. The theorem generalizes known results for the algebra

L
∞

(
Ω
,
Σ
,
μ
)

{L^\infty }(\Omega ,\Sigma ,\mu )

and the space of bounded linear operators on a Hilbert space.
Rings with annihilator chain conditions and right distributive rings
Authors: Ferrero Miguel , Törner Günter
Published: July 2010

We prove that if a right distributive ring

R
R

, which has at least one completely prime ideal contained in the Jacobson radical, satisfies either a.c.c or d.c.c. on principal right annihilators, then the prime radical of

R
R

is the right singular ideal of

R
R

and is completely prime and nilpotent. These results generalize a theorem by Posner for right chain rings.
Coefficients de Fourier de fonctions à variation bornée
Authors: Wu Jie
Published: July 2010

Let

f
:

R

→

C

f:\mathbb {R} \to \mathbb {C}

be a function of period

2
π

2\pi

and of bounded variation on

[
0
,
2
π
]

[0,2\pi ]

with the total variation

V
(
f
)

V(f)

. Its Fourier coefficients are denoted by

f
^

(
n
)

\hat f(n)

. In this short note, we give a very simple proof of the known result
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartAbsoluteValue ModifyingAbove f With caret left-parenthesis n right-parenthesis EndAbsoluteValue less-than-or-slanted-equals upper V left-parenthesis f right-parenthesis slash 2 pi StartAbsoluteValue n EndAbsoluteValue left-parenthesis n element-of double-struck upper Z comma n not-equals 0 right-parenthesis">

|

f
^

(
n
)

|

⩽
V
(
f
)

/

2
π

|

n

|

(
n
∈

Z

,

n
≠
0
)

|\hat f(n)| \leqslant V(f)/2\pi |n|\;(n \in \mathbb {Z},\;n \ne 0)

.
Ratios of regulators in extensions of number fields
Authors: Costa Antone , Friedman Eduardo
Published: July 2010

Let

L

/

K

L/K

be an extension of number fields. Then
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R e g left-parenthesis upper L right-parenthesis slash upper R e g left-parenthesis upper K right-parenthesis greater-than c Subscript left-bracket upper L colon bold upper Q right-bracket Baseline left-parenthesis log StartAbsoluteValue upper D Subscript upper L Baseline EndAbsoluteValue right-parenthesis Superscript m Baseline comma">

Reg
⁡
(
L
)

/

Reg
⁡
(
K
)
>

c

[
L
:

Q

]

(
log
⁡

|

D
L

|

)
m

,

\operatorname {Reg} (L)/\operatorname {Reg} (K) > {c_{[L:{\mathbf {Q}}]}}{(\log |{D_L}|)^m},

\]
where Reg denotes the regulator,

D
L

{D_L}

is the absolute discriminant of

L
L

, and

c

[
L
:

Q

]

>
0

{c_{[L:{\mathbf {Q}}]}} > 0

depends only on the degree of

L
L

. The nonnegative integer

m
=
m
(
L

/

K
)

m = m(L/K)

is positive if

L

/

K

L/K

does not belong to certain precisely defined infinite families of extensions, analogous to CM fields, along which

Reg
⁡
(
L
)

/

Reg
⁡
(
K
)

\operatorname {Reg} (L)/\operatorname {Reg} (K)

is constant. This generalizes some inequalities due to Remak and Silverman, who assumed that

K
K

is the rational field

Q

{\mathbf {Q}}

, and modifies those of Bergé-Martinet, who dealt with a general extension

L

/

K

L/K

but used its relative discriminant where we use the absolute one.
Lower bounds for the L.-S. category of products
Authors: Jessup Barry , Ndombol Bitjong
Published: July 2010

Halperin and Lemaire introduced L.-S. category type invariants

left-

Mcat
⁡
(
A
)

{\text {left-}}\operatorname {Mcat} (A)

and

right-

Mcat
⁡
(
A
)

{\text {right-}}\operatorname {Mcat} (A)

(/l) for certain differential algebras

(
A
,
d
)

(A,d)

. In particular, they proved that if

(
A
,
d
)
=

C

∗

(
S
,
k
)

(A,d) = {C^{\ast }}(S,k)

is the

k
k

-valued singular cochains on

1
1

-connected space

S
S

, then these invariants are lower bounds for the classical category

cat

(
S
)

{\text {cat}}(S)

. We use an explicit model for Ganea’s space due to Felix, Halperin, Lemaire, and Thomas to prove

lMcat
⁡
(
A
⊗
B
)
⩽
lMcat
⁡
(
A
)
+
e
(
B
)

\operatorname {lMcat} (A \otimes B) \leqslant \operatorname {lMcat} (A) + e(B)

, over any field, where

e
e

denotes Toomer’s invariant. This proves Ganea’s conjecture for Mcat over fields of arbitrary characteristic.
A fixed point property of 𝑙₁-product spaces
Authors: Kuczumow Tadeusz , Reich Simeon , Schmidt Malgorzata
Published: July 2010

LetX1{X_1}andX2{X_2}be Banach spaces, and letX1×X2{X_1} \times {X_2}be equipped with thel1{l_1}-norm. If the first spaceX1{X_1}is uniformly convex in every direction, thenX1×X2{X_1} \times {X_2}has the fixed point property for nonexpansive mappings (FPP) if and only ifR×X2\mathbb {R} \times {X_2}(with thel1{l_1}-norm) does. IfX1{X_1}is merely strictly convex,(R×X2)(\mathbb {R} \times {X_2})has the FPP, andCi⊂Xi{C_i} \subset {X_i}are weakly compact and convex with the FPP (fori=1,2i = 1,2), then the fixed point set of every nonexpansive mappingT:C1×C2→C1×C2T:{C_1} \times {C_2} \to {C_1} \times {C_2}is a nonexpansive retract ofC1×C2{C_1} \times {C_2}.
A representation lattice isomorphism for the peripherical spectrum
Authors: Martínez Josep
Published: July 2010

In this paper we construct a representation isometric lattice isomorphism for the peripherical spectrum of a positive operator on a Banach lattice. By a representation lattice homomorphism, we mean that the peripherical spectrum of the operator is identified with the spectrum of the induced isometric lattice homomorphism. A simple proof of a "zero-two" law follows easily from our representation technique.
The integration operator in two variables
Authors: Atzmon A. , Manos H.
Published: July 2010

In this paper we consider the integration operator in two variables on

L
2

[
0
,
1

]
2

{L_2}{[0,1]^2}

, determine its multiplicity and reducing subspaces, and make some observations about its invariant and hyperinvariant subspaces.
Universal filtration of Schur complexes
Authors: Boffi Giandomenico
Published: July 2010

The Schur complex

L

λ

/

μ

ϕ

{{\mathbf {L}}_{\lambda /\mu }}\phi

has proved useful in studying resolutions of determinantal ideals, both in characteristic zero and in a characteristic-free setting. We show here that in every characteristic,

L

λ

/

μ

ϕ

{{\mathbf {L}}_{\lambda /\mu }}\phi

is isomorphic, up to a filtration, to a sum of Schur complexes

∑
ν

γ
(
λ

/

μ
;
ν
)

L

ν

ϕ

\sum \nolimits _\nu {\gamma (\lambda /\mu ;\nu ){{\mathbf {L}}_\nu }\phi }

, where

γ
(
λ

/

μ
;
ν
)

\gamma (\lambda /\mu ;\nu )

is the usual Littlewood-Richardson coefficient. This generalizes a well-known direct sum decomposition of

L

λ

/

μ

ϕ

{{\mathbf {L}}_{\lambda /\mu }}\phi

in characteristic zero.