bluuebunny/crossref_metadata_2025 huggingface dataset:
Toeplitz operators on the polydisk
Authors: Sun Sunhua , Zheng Dechao
Published: July 2002

In this paper it is shown that two analytic Toeplitz operators essentially doubly commute if and only if they doubly commute on the Bergman space of the polydisk.
Images of bilinear mappings into 𝐑³
Authors: Bernau S. , Wojciechowski Piotr
Published: July 2002

It is well-known that the image of a multilinear mapping into a vector space need not be a subspace of its target space. It is, however, far from clear which subsets of the target space may be such images. For vector spaces over the real numbers we give a complete classification of the images of bilinear mappings into a three-dimensional vector space. In Theorem 2.8 we show that either the image of a bilinear mapping into a three-dimensional space is a subspace, or its complement is either the interior of a double elliptic cone, or a plane from which two lines intersecting at the origin have been removed. We also show (Theorem 2.2) that the image of any multilinear mapping into a two-dimensional space is necessarily a subspace. Our methods are elementary and free of tensor considerations.
Irreducible positive linear maps on operator algebras
Authors: Farenick Douglas
Published: July 2002

Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible positive linear maps on von Neumann algebras are explicitly constructed, and a criterion for the irreducibility of decomposable positive maps on full matrix algebras is given.
Expanding the joint spectrum of pairs of commuting contractions
Authors: Ionescu Adrian
Published: July 2002

We present a connection between solving the invariant subspace problem for a single operator 

T
T

on Hilbert space and the existence of a common invariant subspace for two commuting related operators. In particular, we reduce the problem of the existence of nontrivial invariant subspaces for a single contraction with spectral radius one to the problem of the existence of common nontrivial invariant subspaces for a pair of commuting contractions with large joint spectra.
Inducing characters and nilpotent subgroups
Authors: Navarro Gabriel
Published: July 2002

If

H
H

is a subgroup of a finite group

G
G

and

γ
∈
Irr
⁡
(
H
)

\gamma \in \operatorname {Irr}(H)

induces irreducibly up to

G
G

, we prove that, under certain odd hypothesis,

F

(
G
)

F

(
H
)

\mathbf {F}(G) \mathbf {F}(H)

is a nilpotent subgroup of

G
G

.
Stability of semigroups commuting with a compact operator
Authors: Phóng Vũ
Published: July 2002

It is proved that if

T
(
t
)
,
S
(
t
)

T(t), S(t)

are bounded

C

0

C_{0}

-semigroups on Banach spaces

X
X

and

Y
Y

, resp., and

C
:
Y
→
X

C:Y\to X

,

K
:
Y
→
Y

K:Y\to Y

are bounded operators with dense ranges such that

C
C

intertwines

T
(
t
)

T(t)

with

S
(
t
)

S(t)

and

K
K

commutes with

S
(
t
)

S(t)

, then

T
(
t
)

T(t)

is strongly stable provided

A
A

—the generator of

T
(
t
)

T(t)

—does not have eigenvalue on

i

R

i\mathbf {R}

. An analogous result holds for power-bounded operators.
Duality and perfect probability spaces
Authors: Ramachandran D. , Rüschendorf L.
Published: July 2002

Given probability spaces

(

X
i

,

A

i

,

P
i

)
,
i
=
1
,
2
,

(X_i,\mathcal {A}_i,P_i), i=1,2,

let

M

(

P
1

,

P
2

)

\mathcal {M}(P_1,P_2)

denote the set of all probabilities on the product space with marginals

P
1

P_1

and

P
2

P_2

and let

h
h

be a measurable function on

(

X
1

×

X
2

,

A

1

⊗

A

2

)
.

(X_1 \times X_2,\mathcal {A}_1 \otimes \mathcal {A}_2).

Continuous versions of linear programming stemming from the works of Monge (1781) and Kantorovich-Rubinštein (1958) for the case of compact metric spaces are concerned with the validity of the duality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row 1st Column Blank 2nd Column a m p semicolon sup left-brace right-brace colon integral integral h separator d separator upper P colon element-of element-of upper P of MM left-parenthesis right-parenthesis comma upper P 1 comma upper P 2 3rd Column a m p semicolon equals inf left-brace right-brace colon sigma-summation sigma-summation equals equals i 12 integral integral times times times hidPi colon less-than-or-equal-to less-than-or-equal-to element-of element-of hi times times times times times of LL 1 left-parenthesis right-parenthesis Piandh circled-plus circled-plus ihi EndLayout">

a
m
p
;
sup
{
∫
h
d
P
:
P
∈

M

(

P
1

,

P
2

)
}
 

a
m
p
;

=

inf
{

∑

i
=
1

2

∫

h
i

d

P
i

:

h
i

∈

L

1

(

P
i

)

a
n
d

h
≤

⊕

i

h
i

}

\begin{align*} &\sup \{ \int h dP: P \in \mathcal {M}(P_1,P_2) \} \ &\qquad = \: \inf \{ \sum _{i=1}^{2} \int h_i dP_i : h_i \in \mathcal {L}^1 (P_i) \; \; and \; \; h \leq {\oplus }_i h_i\} \end{align*}

(where

M

(

P
1

,

P
2

)

\mathcal {M}(P_1,P_2)

is the collection of all probability measures on

(

X
1

×

X
2

,

A

1

⊗

A

2

)

(X_1 \times X_2, \mathcal {A}_1 \otimes \mathcal {A}_2)

with

P
1

P_1

and

P
2

P_2

as the marginals). A recently established general duality theorem asserts the validity of the above duality whenever at least one of the marginals is a perfect probability space. We pursue the converse direction to examine the interplay between the notions of duality and perfectness and obtain a new characterization of perfect probability spaces.
Again nice equations for nice groups
Authors: Abhyankar Shreeram
Published: July 2002

Nice quartinomial equations are given for unramified coverings of the affine line in nonzero characteristic

p
p

with PSU

(
2
m
−
1
,

q
′

)

(2m-1,q’)

and SU

(
2
m
−
1
,

q
′

)

(2m-1,q’)

as Galois groups where

m
>
1

m>1

is any integer and

q
′

>
1

q’>1

is any power of

p
p

.
Strongly 𝜋-regular rings have stable range one
Authors: Ara Pere
Published: July 2002

A ring

R
R

is said to be strongly

π
\pi

-regular if for every

a
∈
R

a\in R

there exist a positive integer

n
n

and

b
∈
R

b\in R

such that

a

n

=

a

n
+
1

b

a^{n}=a^{n+1}b

. For example, all algebraic algebras over a field are strongly

π
\pi

-regular. We prove that every strongly

π
\pi

-regular ring has stable range one. The stable range one condition is especially interesting because of Evans’ Theorem, which states that a module

M
M

cancels from direct sums whenever

End

R

(
M
)

\text {End}_{R} (M)

has stable range one. As a consequence of our main result and Evans’ Theorem, modules satisfying Fitting’s Lemma cancel from direct sums.
Minimal upper bounds of commuting operators
Authors: Akemann Charles , Weaver Nik
Published: July 2002

Let

(

x

i

)

(x_{i})

be a finite collection of commuting self-adjoint elements of a von Neumann algebra

M

\mathcal {M}

. Then within the (abelian) C*-algebra they generate, these elements have a least upper bound

x
x

. We show that within

M

\mathcal {M}

,

x
x

is a minimal upper bound in the sense that if

y
y

is any self-adjoint element such that

x

i

≤
y
≤
x

x_{i} \leq y \leq x

for all

i
i

, then

y
=
x

y = x

. The corresponding assertion for infinite collections

(

x

i

)

(x_{i})

is shown to be false in general, although it does hold in any finite von Neumann algebra. We use this sort of result to show that if

N

⊂

M

\mathcal {N} \subset \mathcal {M}

are von Neumann algebras,

Φ
:

M

→

N

\Phi : \mathcal {M} \to \mathcal {N}

is a faithful conditional expectation, and

x
∈

M

x \in \mathcal {M}

is positive, then

Φ
(

x

n

)

1

/

n

\Phi (x^{n})^{1/n}

converges in the strong operator topology to the “spectral order majorant” of

x
x

in

N

\mathcal {N}

.
Generalized Cuntz-Krieger algebras
Authors: Deaconu Valentin
Published: July 2002

To a special embedding

Φ
\Phi

of circle algebras having the same spectrum, we associate an r-discrete, locally compact groupoid, similar to the Cuntz-Krieger groupoid. Its

C

∗

\mathbf {C}^*

-algebra, denoted

O

Φ

\mathcal {O}_{\Phi }

, is a continuous version of the Cuntz-Krieger algebras

O

A

\mathcal {O}_A

. The algebra

O

Φ

\mathcal {O}_{\Phi }

is generated by an AT-algebra and a nonunitary isometry. We compute its K-theory under the assumption that the AT-algebra is simple.
A simple proof of Singer’s representation theorem
Authors: Hensgen Wolfgang
Published: July 2002

Let

Ω
\Omega

be a compact Hausdorff space and

X
X

a Banach space. Singer’s theorem states that under the dual pairing

(
f
,
m
)
↦
∫
⟨
f
,
d
m
⟩

(f,m)\mapsto \int \langle f,dm\rangle

, the dual space of

C
(
Ω
;
X
)

C(\Omega ;X)

is isometric to

r
c
a
b
v
(
Ω
;

X
′

)

rcabv (\Omega ;X’)

. Using the Hahn-Banach theorem and the (scalar) Riesz representation theorem, a proof of Singer’s theorem is given which appears to be simpler than the proofs supplied earlier by Singer (1957, 1959) and Dinculeanu (1959, 1967).
Classifying spaces and homotopy sets of axes of pairings
Authors: Ishiguro Kenshi
Published: July 2002

We consider the maps between classifying spaces of the form

B
K
×
B
L
→
B
G

BK \times BL \rightarrow BG

. The main theorem shows that if the restriction map on

B
L

BL

is a weak epimorphism, then the restriction on

B
K

BK

should factor through the classifying spaces of the center of the compact Lie group

G
G

. An application implies that

B
G

BG

is an H–space (Hopf space) if and only if

G
G

is abelian.
Existence for a matrix equation arising in microelectronics
Authors: Juang Jonq
Published: July 2002

In this paper we rigorously show the existence of solutions of a matrix equation which arises in the design of micro electronical circuits. This equation was studied by Szidarovszky and Palusinsk [Appl. Math. Comput. 64, 115-119(1994)], who also presented an iterative algorithm for its solution. We show, via an example, that this algorithm could converge extremely slow in certian cases. The solution can then be used to minimize the reflection coefficients of the active signals.
Characterization of classical groups by orbit sizes on the natural module
Authors: Liebeck Martin
Published: July 2002

We show that if

V
V

is a finite vector space, and

G
G

is a subgroup of

P
Γ
L
(
V
)

P\Gamma L(V)

having the same orbit sizes on 1-spaces as an orthogonal or unitary group on

V
V

, then, with a few exceptions,

G
G

is itself an orthogonal or unitary group on

V
V

.
Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps
Authors: Martens Marco , Tresser Charles
Published: July 2002

We prove that for continuous maps on the interval, the existence of an

n
n

-cycle implies the existence of

n
−
1

n-1

points which interwind the original ones and are permuted by the map. We then use this combinatorial result to show that piecewise affine maps (with no zero slope) cannot be infinitely renormalizable.
Harmonic measure, infinite kernels, and symmetrization
Authors: Velling John
Published: July 2002

The vanishing of area for the infinite Nielsen kernel of an arbitrary open Riemann surface is shown to follow from iteration of a natural geometric operation on the unit disk. This operation compares the distribution of harmonic measure on the boundaries of two related simply connected domains, and is not yet sufficiently well understood.
Generalized evaluation subgroups of product spaces relative to a factor
Authors: Lee Kee , Woo Moo
Published: July 2002

For any

C
W

CW

-complexes

X
X

and

Y
Y

, we show that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G Subscript n Baseline left-parenthesis upper X times upper Y comma upper X right-parenthesis equals upper G Subscript n Baseline left-parenthesis upper X right-parenthesis circled-plus pi Subscript n Baseline left-parenthesis upper Y right-parenthesis">

G

n

(
X
×
Y
,
X
)
=

G

n

(
X
)
⊕

π

n

(
Y
)

G_{n}(X \times Y, X) = G_{n}(X) \oplus \pi _{n}(Y)

. We use this fact to compute generalized evaluation subgroups of generalized tori relative to a sphere.
A closed model category for (𝑛-1)-connected spaces
Authors: Aldana J. , Paricio L. , Rodríguez M.
Published: July 2002

For each integer

n
>
0

n > 0

, we give a distinct closed model category structure to the category of pointed spaces

Top
⋆

\operatorname {Top}_\star

such that the corresponding localized category

Ho
⁡
(

Top
⋆
n

)

\operatorname {Ho}(\operatorname {Top}_\star ^n)

is equivalent to the standard homotopy category of

(
n
−
1
)

(n-1)

-connected CW-complexes. The structure of closed model category given by Quillen to

Top
⋆

\operatorname {Top}_\star

is based on maps which induce isomorphisms on all homotopy group functors

π
q

\pi _q

and for any choice of base point. For each

n
>
0

n>0

, the closed model category structure given here takes as weak equivalences those maps that for the given base point induce isomorphisms on

π
q

\pi _q

for

q
≥
n

q\ge n

.
A small Dowker space in ZFC
Authors: Balogh Zoltan
Published: July 2002

We construct a hereditarily normal topological space whose product with the unit interval is not normal. The space is

σ
\sigma

-relatively discrete and has cardinality of the continuum

c

\mathfrak {c}

.
Bounding families of ruled surfaces
Authors: Gallego Francisco , Giraldo Luis , Sols Ignacio
Published: July 2002

In this paper we provide a sharp bound for the dimension of a family of ruled surfaces of degree

d
d

in

P

K

3

\mathbf P_{\mathbf K}^3

. We also find the families with maximal dimension: the family of ruled surfaces containing two unisecant skew lines, when

d
≥
9

d\ge 9

and the family of rational ruled surfaces, when

d
≤
9

d\le 9

.

The first tool we use is a Castelnuovo-type bound for the irregularity of ruled surfaces in

P

K

n

\mathbf P_{\mathbf K}^n

. The second tool is an exact sequence involving the normal sheaf of a curve in the grassmannian. This sequence is analogous to the one constructed by Eisenbud and Harris in 1992, where they deal with the problem of bounding families of curves in projective space. However, our construction is more general since we obtain the mentioned sequence by purely algebraic means, studying the geometry of ruled surfaces and of the grassmannian.
On the Picard group of a compact flat projective variety
Authors: Michelacakis N.
Published: July 2002

In this note, we describe the Picard group of the class of compact, smooth, flat, projective varieties. In view of Charlap’s work and Johnson’s characterization, we construct line bundles over such manifolds as the holonomy-invariant elements of the Neron-Severi group of a projective flat torus covering the manifold. We prove a generalized version of the Appell-Humbert theorem which shows that the nontrivial elements of the Picard group are precisely those coming from the above construction. Our calculations finally give an estimate for the set of positive line bundles for such varieties.
A non-treelike continuum that is not the 2-to-1 image of any continuum
Authors: Heath Jo
Published: July 2002

Some thirteen years ago S. B. Nadler, Jr. and L. E. Ward, Jr., asked if any treelike continuum could be the 2-to-1 image of a continuum. In fact, it has been conjectured that the property of being treelike characterizes those continua that are not the 2-to-1 image of any continuum. But the characterization must be something else; this paper shows that many pseudo-solenoids are not the 2-to-1 image of any continuum.
Shift-invariant spaces on the real line
Authors: Jia Rong-Qing
Published: July 2002

We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in

L
p

(

R

)

L_p(\mathbb {R})

(
1
≤
p
≤
∞
)

(1\le p\le \infty )

. Based on a study of linear independence of the shifts of the generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on

Z

\mathbb {Z}

. Moreover, we show that such a shift-invariant space provides

L
p

L_p

-approximation order

k
k

if and only if it contains all polynomials of degree less than

k
k

.
The 𝐷-resultant, singularities and the degree of unfaithfulness
Authors: van den Essen Arno , Yu Jie-Tai
Published: July 2002

We introduce the

D
D

-resultant of two polynomials in one variable and show how it can be used to decide if
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="k left-parenthesis f left-parenthesis t right-parenthesis comma g left-parenthesis t right-parenthesis right-parenthesis equals k left-parenthesis t right-parenthesis comma k left-bracket f left-parenthesis t right-parenthesis comma g left-parenthesis t right-parenthesis right-bracket equals k left-bracket t right-bracket">

k
(
f
(
t
)
,
g
(
t
)
)
=
k
(
t
)
,
k
[
f
(
t
)
,
g
(
t
)
]
=
k
[
t
]

k(f(t),g(t))=k(t),k[f(t),g(t)]=k[t]

and to find the singularities of the curve

x
=
f
(
t
)
,
y
=
g
(
t
)

x=f(t),y=g(t)

. The second criterion is used to give a very short proof of a special case of the epimorphism theorem of Abhyankar and Moh.
Distinct differentiable functions may share the same Clarke subdifferential at all points
Authors: Borwein J. , Wang Xianfu
Published: July 2002

We construct, using Zahorski’s Theorem, two everywhere differentiable real–valued Lipschitz functions differing by more than a constant but sharing the same Clarke subdifferential and the same approximate subdifferential.
Wilson’s functional equation for vector and matrix functions
Authors: Sinopoulos Pavlos
Published: July 2002

We determine the general solution of the functional equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis x plus y right-parenthesis plus f left-parenthesis x minus y right-parenthesis equals upper A left-parenthesis y right-parenthesis f left-parenthesis x right-parenthesis left-parenthesis x comma y element-of upper G right-parenthesis comma">

f
(
x
+
y
)
+
f
(
x
−
y
)
=
A
(
y
)
f
(
x
)

(
x
,
y
∈
G
)
,

f(x+y)+f(x-y) =A(y)f(x)\qquad (x,y\in G),

\]
where

G
G

is a 2-divisible abelian group,

f
f

is a vector-valued function and

A
A

is a matrix-valued function. Using this result we solve the scalar equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis x plus y right-parenthesis plus f left-parenthesis x minus y right-parenthesis equals g 1 left-parenthesis x right-parenthesis h 1 left-parenthesis y right-parenthesis plus g 2 left-parenthesis x right-parenthesis h 2 left-parenthesis y right-parenthesis left-parenthesis x comma y element-of upper G right-parenthesis comma">

f
(
x
+
y
)
+
f
(
x
−
y
)
=

g
1

(
x
)

h
1

(
y
)
+

g
2

(
x
)

h
2

(
y
)

(
x
,
y
∈
G
)
,

f(x+y)+f(x-y)=g_1(x)h_1(y)+g_2(x) h_2(y)\qquad (x,y\in G),

\]
which contains as special cases, among others, the d’Alembert and Wilson equations and the parallelogram law.
Analysis of the Wu metric II: The case of non-convex Thullen domains
Authors: Cheung C. , Kim K.
Published: July 2002

We present an explicit description of the Wu invariant metric on the non-convex Thullen domains. We show that the Wu invariant Hermitian metric, which in general behaves as nicely as the Kobayashi metric under holomorphic mappings, enjoys better regularity in this case. Furthermore, we show that the holomorphic curvature of the Wu metric is bounded from above everywhere by

−
1

/

2

-1/2

. This leads the Wu metric to be a natural solution to a conjecture of Kobayashi in the case of non-convex Thullen domains.
The first instability interval for Hill equations with symmetric single well potentials
Authors: Huang Min-Jei
Published: July 2002

For Hill equations with symmetric single well (or symmetric single barrier) potentials, the first instability interval is absent when and only when the potential is constant.
𝐽-holomorphic curves in almost complex surfaces do not always minimize the genus
Authors: Mikhalkin G.
Published: July 2002

The adjunction formula computes the genus of an almost complex curve

F
F

embedded in an almost complex surface

M
M

in terms of the homology class of

F
F

. If

M
M

is Kähler (or at least symplectic) and the self-intersection of

F
F

is non-negative then the genus of any other surface embedded in

M
M

and homologous to

F
F

is not less then the genus of

F
F

(the proof of this statement (which is a generalization of the Thom conjecture for

C

P
2

\Bbb C P^2

) was recently given by the Seiberg-Witten theory). This paper shows that the extra assumptions on

M
M

are essential for the genus-minimizing properties of embedded almost complex curves.
Hopfian and co-Hopfian 𝐺-CW-complexes
Authors: Mukherjee Goutam
Published: July 2002

We determine conditions for a

G
G

-CW-complex to be a Hopfian or a co-Hopfian object in the

G
G

-homotopy category of

G
G

-path-connected

G
G

-CW-complexes with base points.
A relation between the pluricomplex and the classical Green functions in the unit ball of 𝐂ⁿ
Authors: Carlehed Magnus
Published: July 2002

We give a sharp upper bound for the quotient of the pluricomplex and the classical Green functions in the unit ball ofCn\mathbf {C}^n.
Local fundamental groups of algebraic varieties
Authors: Abhyankar Shreeram
Published: July 2002

Some progress is made in the calculation of local fundamental groups.
Projective polynomials
Authors: Abhyankar Shreeram
Published: July 2002

Certain nice trinomials have the projective linear groups as their Galois groups. This was proved using considerable group theory. Here is an easier proof based on the observation that the said trinomials are what may be called projective polynomials. It extends the results to a local situation.
A new subcontinuum of 𝛽ℝ\ℝ
Authors: Dow Alan , Hart Klaas
Published: July 2002

We present a method for describing all indecomposable subcontinua of 

β

R

∖

R

\beta \mathbb {R}\setminus \mathbb {R}

. This method enables us to construct in 

Z
F
C

\mathsf {ZFC}

a new subcontinuum of 

β

R

∖

R

\beta \mathbb {R}\setminus \mathbb {R}

. We also show that the nontrivial layers of standard subcontinua can be described by our method. This allows us to construct a layer with a proper dense

F
σ

F_\sigma

-subset and bring the number of (known) nonhomeomorphic subcontinua of 

β

R

∖

R

\beta \mathbb {R}\setminus \mathbb {R}

to 14.
Rigidity of compact manifolds with boundary and nonnegative Ricci curvature
Authors: Xia Changyu
Published: July 2002

Let

Ω
¯

\overline {\Omega }

be an (

n
+
1

n+1

)-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary

M
=
∂

Ω
¯

M=\partial \overline {\Omega }

. Assume that the principal curvatures of

M
M

are bounded from below by a positive constant

c
c

. In this paper, we prove that the first nonzero eigenvalue

λ

1

\lambda _{1}

of the Laplacian of

M
M

acting on functions on

M
M

satisfies

λ

1

≥
n

c

2

\lambda _{1} \geq nc^{2}

with equality holding if and only if

Ω
\Omega

is isometric to an

(
n
+
1
)

(n+1)

-dimensional Euclidean ball of radius

1
c

\frac {1}{c}

. Some related rigidity theorems for

Ω
¯

\overline {\Omega }

are also proved.
Norm attaining functionals on 𝐶(𝑇)
Authors: Kenderov P. , Moors W. , Sciffer Scott
Published: July 2002

It is shown that for any infinite compact Hausdorff space

T
T

, the Bishop-Phelps set in

C
(
T

)
∗

C(T)^*

is of the first Baire category when

C
(
T
)

C(T)

has the supremum norm.
Zero divisors and 𝐿^{𝑝}(𝐺)
Authors: Puls Michael
Published: July 2002

Let

G
G

be a discrete group,

C

G

\mathbb {C}G

the group ring of

G
G

over

C

\mathbb {C}

and

L
p

(
G
)

L^p(G)

the Lebesgue space of

G
G

with respect to Haar measure. It is known that if

G
G

is torsion free elementary amenable,

0
≠
α
∈

C

G

0\ne \alpha \in \mathbb {C}G

and

0
≠
β
∈

L
2

(
G
)

0\ne \beta \in L^2(G)

, then

α
∗
β
≠
0

\alpha *\beta \ne 0

. We will give a sufficient condition for this to be true when

p
>
2

p>2

, and in the case

G
=

Z

n

G=\mathbb {Z}^n

we will give sufficient conditions for this to be false when

p
>
2

p>2

.
On uniqueness of invariant means
Authors: Bekka M.
Published: July 2002

The following results on uniqueness of invariant means are shown: (i) Let

G

\mathbb {G}

be a connected almost simple algebraic group defined over

Q

\mathbb {Q}

. Assume that

G

(

R

)

\mathbb {G}(\mathbb {R})

, the group of the real points in

G

\mathbb {G}

, is not compact. Let

p
p

be a prime, and let

G

(

Z

p

)

\mathbb {G}({\mathbb {Z}}_{p})

be the compact

p
p

-adic Lie group of the

Z

p

{\mathbb {Z}}_{p}

–points in

G

\mathbb {G}

. Then the normalized Haar measure on

G

(

Z

p

)

\mathbb {G}({\mathbb {Z}}_{p})

is the unique invariant mean on

L

∞

(

G

(

Z

p

)
)

L^{\infty }(\mathbb {G}({\mathbb {Z}}_{p}))

. (ii) Let

G
G

be a semisimple Lie group with finite centre and without compact factors, and let

Γ
\Gamma

be a lattice in

G
G

. Then integration against the

G
G

–invariant probability measure on the homogeneous space

G

/

Γ

G/\Gamma

is the unique

Γ
\Gamma

–invariant mean on

L

∞

(
G

/

Γ
)

L^{\infty } (G/\Gamma )

.
Corrected outer functions
Authors: Doubtsov Evgueni
Published: July 2002

Given

0
>
p
>
2

0>p>2

and a strictly positive continuous function

φ
\varphi

on the unit circle, we construct a bounded analytic function

g
g

such that

|

g

∗

|

=
φ

|g^{*}|=\varphi

a.e., and

g
g

is in the Besov space

A

p

1

A_{p}^{1}

on the unit disc.
A weighted Poincaré inequality with a doubling weight
Authors: Hurri-Syrjānen Ritva
Published: July 2002

We show that unbounded John domains (and even a larger class of domains than John domains) satisfy the weighted Poincaré inequality
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="inf Underscript a element-of double-struck upper R Endscripts double-vertical-bar u left-parenthesis x right-parenthesis minus a double-vertical-bar Subscript upper L Sub Superscript q Subscript left-parenthesis upper D comma w 1 right-parenthesis Baseline less-than-or-equal-to upper C double-vertical-bar nabla u left-parenthesis x right-parenthesis double-vertical-bar Subscript upper L Sub Superscript p Subscript left-parenthesis upper D comma w 2 right-parenthesis">

inf

a
∈

R

‖
u
(
x
)
−
a

‖

L

q

(
D
,

w

1

)

≤
C
‖
∇
u
(
x
)

‖

L

p

(
D
,

w

2

)

\begin{equation*}\inf _{a\in \mathbb {R}} \|u(x)-a\|_{L^{q}(D,w_{1})} \le C\|\nabla u(x)\|_{L^{p}(D,w_{2})}\end{equation*}

whenever

u
u

is a Lipschitz function on

D
D

,

w

1

w_{1}

is a doubling weight, and weights satisfy certain cube conditions, and

C
=
C
(
D
,
p
,
q
,

w

1

,

w

2

)

C=C(D,p,q,w_{1},w_{2})

.
On the dilatation of univalent planar harmonic mappings
Authors: Weitsman Allen
Published: July 2002

It is shown that if

f
f

is a univalent harmonic mapping of the unit disk onto a domain having a smooth boundary arc which is convex with respect to the domain, and if the dilatation has modulus 1 on the arc, then the arc must be a line segment.
Stability of weakly almost conformal mappings
Authors: Yan Baisheng , Zhou Zhengfang
Published: July 2002

We prove a stability of weakly almost conformal mappings in

W

1
,
p

(
Ω
;

R

n

)

W^{1, p}(\Omega ;\mathbf {R}^n)

for

p
p

not too far below the dimension

n
n

by studying the

W

1
,
p

W^{1, p}

-quasiconvex hull of the set

C

n

\mathcal C_n

of conformal matrices. The study is based on coercivity estimates from the nonlinear Hodge decompositions and reverse Hölder inequalities from the Ekeland variational principle.
Vector moment problems for rapidly decreasing smooth functions of several variables
Authors: Estrada Ricardo
Published: July 2002

The existence of rapidly decreasing smooth solutions of moment problems for functions of several variables with values in a Fréchet space is obtained. It is shown that the corresponding results for functions with values in a general topological vector space do not hold.
Crossed products of Hilbert C*-bimodules by countable discrete groups
Authors: Kajiwara Tsuyoshi , Watatani Yasuo
Published: July 2002

We introduce a notion of crossed products of Hilbert C

∗

{}^{*}

-bimodules by countable discrete groups and mainly study the case of finite groups following Jones index theory. We give a sufficient condition such that the crossed product bimodule is irreducible. We have a bimodule version of Takesaki-Takai duality. We show the categorical structures when the action is properly outer, and give some example of this construction concerning the orbifold constructions.
Subnormal subgroups of group ring units
Authors: Marciniak Zbigniew , Sehgal Sudarshan
Published: July 2002

Let

G
G

be an arbitrary group. If

a
∈

Z

G

a\in \mathbb {Z}G

satisfies

a

2

=
0

a^{2}=0

,

a
≠
0

a\ne 0

, then the units

1
+
a

1+a

,

1
+

a

∗

1+a^{*}

generate a nonabelian free subgroup of units. As an application we show that if

G
G

is contained in an almost subnormal subgroup

V
V

of units in

Z

G

\mathbb {Z}G

then either

V
V

contains a nonabelian free subgroup or all finite subgroups of

G
G

are normal. This was known before to be true for finite groups

G
G

only.
On Stone’s theorem and the Axiom of Choice
Authors: Good C. , Tree I. , Watson W.
Published: July 2002

It is a well established fact that in Zermelo-Fraenkel set theory, Tychonoff’s Theorem, the statement that the product of compact topological spaces is compact, is equivalent to the Axiom of Choice. On the other hand, Urysohn’s Metrization Theorem, that every regular second countable space is metrizable, is provable from just the ZF axioms alone. A. H. Stone’s Theorem, that every metric space is paracompact, is considered here from this perspective. Stone’s Theorem is shown not to be a theorem in ZF by a forcing argument. The construction also shows that Stone’s Theorem cannot be proved by additionally assuming the Principle of Dependent Choice.
Coding nested mixing one-sided subshifts of finite type as Markov shifts having exactly the same alphabet
Authors: Maass Alejandro , Martínez Servet
Published: July 2002

Let

X

0

X_{0}

,

X
X

be mixing one-sided subshifts of finite type such that

X

0

⊆
X

X_{0}\subseteq X

. We show a necessary and sufficient condition for the existence of mixing Markov shifts

Y

0

Y_{0}

,

Y
Y

,

Y

0

⊆
Y

Y_{0}\subseteq Y

, and a conjugacy

π
:
Y
→
X

\pi : Y\to X

with

π
(

Y

0

)
=

X

0

\pi (Y_{0})=X_{0}

, such that the sets of letters appearing in both systems are the same, more precisely,

L

1

(

Y

0

)
=

L

1

(
Y
)

L_{1}(Y_{0})=L_{1}(Y)

.
Neither first countable nor Cech-complete spaces are maximal Tychonoff connected
Authors: Shakhmatov D. , Tkačenko M. , Tkachuk V. , Watson S. , Wilson R.
Published: July 2002

A connected Tychonoff space

X
X

is called maximal Tychonoff connected if there is no strictly finer Tychonoff connected topology on

X
X

. We show that if

X
X

is a connected Tychonoff space and

X
∈
{

X\in \{

locally separable spaces, locally Čech-complete spaces, first countable spaces

}
\}

, then

X
X

is not maximal Tychonoff connected. This result is new even in the cases where

X
X

is compact or metrizable.
Composition operators that improve integrability on weighted Bergman spaces
Authors: Smith Wayne , Yang Liming
Published: July 2002

Composition operators between weighted Bergman spaces with a smaller exponent in the target space are studied. An integrability condition on a generalized Nevanlinna counting function of the inducing map is shown to characterize both compactness and boundedness of such an operator. Composition operators mapping into the Hardy spaces are included by making particular choices for the weights.
Common zeros of theta functions and central Hecke L-values of CM number fields of degree 4
Authors: Yang Tonghai
Published: July 2002

In this note, we apply the method of Rodriguez Villegas and Yang (1996) to construct a family of infinite many theta series over the Hilbert-Blumenthal modular surfaces with a common zero. We also relate the non- vanishing of the central L-values of certain Hecke characters of non-biquadratic CM number fields of degree 4 to the nonvanishing of theta functions at CM points in the Hilbert-Blumenthal modular surfaces.
Foliations of some 3-manifolds which fiber over the circle
Authors: Cooper D. , Long D.
Published: July 2002

We show that a hyperbolic punctured torus bundle admits a foliation by lines which is covered by a product foliation. Thus its fundamental group acts freely on the plane.
A characterization for spaces of sections
Authors: Manoharan Palanivel
Published: July 2002

The space of smooth sections of a bundle over a compact smooth manifold

K
K

can be equipped with a manifold structure, called an

A
A

-manifold, where

A
A

represents the Fréchet algebra of real valued smooth functions on

K
K

. We prove that the

A
A

-manifold structure characterizes the spaces of sections of bundles over

K
K

and its open subspaces. We also describe the

A

(
r
)

A^{(r)}

-maps between

A
A

-manifolds.
Tori in certain aspherical four-manifolds
Authors: Edmonds Allan
Published: July 2002

The homology classes represented by embedded or mapped tori in the product of two surfaces are completely characterized.
𝑃-convexity of Orlicz-Bochner spaces
Authors: Kolwicz Paweł , Płuciennik Ryszard
Published: July 2002

A characterization of

P
P

-convexity of arbitrary Banach space is given. Moreover, it is proved that the Orlicz-Bochner function space

L
L

Φ

(
μ
,
X
)

_\Phi (\mu ,X)

is P-convex if and only if both spaces

L
Φ

(
μ
)

L_\Phi (\mu )

and

X
X

are

P
P

-convex. In particular, the Lebesgue-Bochner space

L
p

(
μ
,
X
)

L^p(\mu ,X)

with

1
>
p
>
∞

1>p>\infty

is

P
P

-convex iff

X
X

is

P
P

-convex.
Finite Euclidean graphs over rings
Authors: Medrano A. , Myers P. , Stark H. , Terras A.
Published: July 2002

We consider graphs attached to

(

Z

/

q

Z

)
n

(\mathbb {Z}/q\mathbb {Z})^n

, where

q
=

p
r

q=p^r

, for an odd prime

p
p

, using an analogue of the Euclidean distance. These graphs are shown to be mostly non-Ramanujan, in contrast to the case of Euclidean graphs over finite fields.
A note on the reducibility of automorphisms of the Klein curve and the 𝜂-invariant of mapping tori
Authors: Morifuji Takayuki
Published: July 2002

We give a characterization for the reducibility of automorphisms of the genus 3 Klein curve in terms of the

η
\eta

-invariant of finite order mapping tori.
Homogeneous ideals in Wick *-algebras
Authors: Proskurin Daniil
Published: July 2002

The necessary and sufficient condition for the family of homogeneous elements to determine a Wick ideal is presented. The structure of homogeneous Wick ideals with degree higher than 2 is discussed. For the braided operator

T
T

a formula to calculate the largest cubic ideal when the quadratic one is known is obtained. Irreducible

∗
*

-representations of the

μ
\mu

-CAR algebra are classified.
Ideal and subalgebra coefficients
Authors: Robbiano Lorenzo , Sweedler Moss
Published: July 2002

For an ideal or

K
K

-subalgebra

E
E

of

K
[

X
1

,
…
,

X
n

]

K[X_1,\dots ,X_n]

, consider subfields

k
⊂
K

k\subset K

, where

E
E

is generated – as ideal or

K
K

-subalgebra – by polynomials in

k
[

X
1

,
…
,

X
n

]

k[X_1,\dots ,X_n]

. It is a standard result for ideals that there is a smallest such

k
k

. We give an algorithm to find it. We also prove that there is a smallest such

k
k

for

K
K

-subalgebras. The ideal results use reduced Gröbner bases. For the subalgebra results we develop and then use subduced SAGBI (bases), the analog to reduced Gröbner bases.
A remark on normal derivations
Authors: Duggal B.
Published: July 2002

Given a Hilbert space

H
H

, let

A
,
S

A,S

be operators on

H
H

. Anderson has proved that if

A
A

is normal and

A
S
=
S
A

AS=SA

, then

‖
A
X
−
X
A
+
S
‖
≥
‖
S
‖

\|AX-XA+S\|\ge \|S\|

for all operators

X
X

. Using this inequality, Du Hong-Ke has recently shown that if (instead)

A
S
A
=
S

ASA=S

, then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar upper A upper X upper A minus upper X plus upper S double-vertical-bar greater-than-or-equal-to double-vertical-bar upper A double-vertical-bar Superscript negative 2 Baseline double-vertical-bar upper S double-vertical-bar">

‖
A
X
A
−
X
+
S
‖
≥
‖
A

‖

−
2

‖
S
‖

\|AXA-X+S\|\ge \|A\|^{-2}\|S\|

for all operators

X
X

. In this note we improve the Du Hong-Ke inequality to

‖
A
X
A
−
X
+
S
‖
≥
‖
S
‖

\|AXA-X+S\|\ge \|S\|

for all operators

X
X

. Indeed, we prove the equivalence of Du Hong-Ke and Anderson inequalities, and show that the Du Hong-Ke inequality holds for unitarily invariant norms.
The sharp Sobolev inequality and the Banchoff-Pohl inequality on surfaces
Authors: Howard Ralph
Published: July 2002

Let

(
M
,
g
)

(M,g)

be a complete two dimensional simply connected Riemannian manifold with Gaussian curvature

K
≤
−
1

K\le -1

. If

f
f

is a compactly supported function of bounded variation on

M
M

, then

f
f

satisfies the Sobolev inequality
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4 pi integral Underscript upper M Endscripts f squared d upper A plus left-parenthesis integral Underscript upper M Endscripts StartAbsoluteValue f EndAbsoluteValue d upper A right-parenthesis squared less-than-or-equal-to left-parenthesis integral Underscript upper M Endscripts double-vertical-bar nabla f double-vertical-bar d upper A right-parenthesis squared period">

4
π

∫
M

f
2

d
A
+

(

∫
M

|

f

|

d
A
)

2

≤

(

∫
M

‖
∇
f
‖

d
A
)

2

.

4\pi \int _M f^2\,dA+ \left (\int _M |f|\,dA \right )^2\le \left (\int _M\|\nabla f\|\,dA \right )^2.

\]
Conversely, letting

f
f

be the characteristic function of a domain

D
⊂
M

D\subset M

recovers the sharp form

4
π
A
(
D
)
+
A
(
D

)
2

≤
L
(
∂
D

)
2

4\pi A(D)+A(D)^2\le L(\partial D)^2

of the isoperimetric inequality for simply connected surfaces with

K
≤
−
1

K\le -1

. Therefore this is the Sobolev inequality “equivalent” to the isoperimetric inequality for this class of surfaces. This is a special case of a result that gives the equivalence of more general isoperimetric inequalities and Sobolev inequalities on surfaces. Under the same assumptions on

(
M
,
g
)

(M,g)

, if

c
:
[
a
,
b
]
→
M

c\colon [a,b]\to M

is a closed curve and

w
c

(
x
)

w_c(x)

is the winding number of

c
c

about

x
x

, then the Sobolev inequality implies
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="4 pi integral Underscript upper M Endscripts w Subscript c Superscript 2 Baseline d upper A plus left-parenthesis integral Underscript upper M Endscripts StartAbsoluteValue w Subscript c Baseline EndAbsoluteValue d upper A right-parenthesis squared less-than-or-equal-to upper L left-parenthesis c right-parenthesis squared comma">

4
π

∫
M

w
c
2

d
A
+

(

∫
M

|

w
c

|

d
A
)

2

≤
L
(
c

)
2

,

4\pi \int _M w_c^2\,dA+ \left (\int _M|w_c|\,dA \right )^2\le L(c)^2,

\]
which is an extension of the Banchoff-Pohl inequality to simply connected surfaces with curvature

≤
−
1

\le -1

.
Central extensions of some Lie algebras
Authors: Li Wanglai , Wilson Robert
Published: July 2002

We consider three Lie algebras:

D
e
r

C

(
(
t
)
)

Der \mathbb {C}((t))

, the Lie algebra of all derivations on the algebra

C

(
(
t
)
)

\mathbb {C}((t))

of formal Laurent series; the Lie algebra of all differential operators on

C

(
(
t
)
)

\mathbb {C}((t))

; and the Lie algebra of all differential operators on

C

(
(
t
)
)
⊗

C

n

.

\mathbb {C}((t))\otimes \mathbb {C}^n.

We prove that each of these Lie algebras has an essentially unique nontrivial central extension.
A structural result of irreducible inclusions of type 𝐼𝐼𝐼_{𝜆} factors, 𝜆∈(0,1)
Authors: Loi Phan
Published: July 2002

Given an irreducible inclusion of factors with finite index

N
⊂
M

N\subset M

, where

M
M

is of type

I
I
I

λ

1

/

m

{III}_{\lambda ^{1/m}}

,

N
N

of type

I
I
I

λ

1

/

n

{III}_{\lambda ^{1/n}}

,

0
>
λ
>
1

0>\lambda >1

, and

m
,
n

m,n

are relatively prime positive integers, we will prove that if

N
⊂
M

N\subset M

satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with

N
⊂
M

N\subset M

. Relations between

N
⊂
M

N\subset M

and a certain

G
G

-kernel on subfactors are also discussed.
The Fuglede-Putnam theorem and a generalization of Barría’s lemma
Authors: Okuyama Toshihiro , Watanabe Keiichi
Published: July 2002

Let

A
A

and

B
B

be bounded linear operators, and let

C
C

be a partial isometry on a Hilbert space. Suppose that (1)

C
A
=
B
C

CA=BC

, (2)

‖
A
‖
≥
‖
B
‖

\|A\|\ge \|B\|

, (3)

(

C
∗

C
)
A
=
A
(

C
∗

C
)

(C^*C)A=A(C^*C)

and (4)

C
(
‖
A

‖
2

−
A

A
∗

)

1

/

2

=
0

C(\|A\|^2-AA^*)^{1/2}=0

. Then we have

C

A
∗

=

B
∗

C

CA^*=B^*C

.
Bordism of two commuting involutions
Authors: Pergher Pedro
Published: July 2002

In this paper we obtain conditions for a Whitney sum of three vector bundles over a closed manifold,

ε

1

⊕

ε

2

⊕

ε

3

→
F

\varepsilon _{1} \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F

, to be the fixed data of a

(

Z

2

)

2

(Z_{2})^{2}

-action; these conditions yield the fact that if

(

ε

1

⊕
R
)
⊕

ε

2

⊕

ε

3

→
F

(\varepsilon _{1} \oplus R) \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F

is the fixed data of a

(

Z

2

)

2

(Z_{2})^{2}

-action, where

R
→
F

R \rightarrow F

is the trivial one dimensional bundle, then the same is true for

ε

1

⊕

ε

2

⊕

ε

3

→
F

\varepsilon _{1} \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F

. The results obtained, together with techniques previously developed, are used to obtain, up to bordism, all possible

(

Z

2

)

2

(Z_{2})^{2}

-actions fixing the disjoint union of an even projective space and a point.
Reducibility of translates of Dickson polynomials
Authors: Turnwald Gerhard
Published: July 2002

Let

K
K

be a field and

a
,
b
∈
K

a,b\in K

. The Dickson polynomial

D

n

(
x
,
a
)

D_{n}(x,a)

is characterized by the equation

D

n

(
x
+
(
a

/

x
)
,
a
)
=

x

n

+
(
a

/

x

)

n

D_{n}(x+(a/x),a)=x^{n}+ (a/x)^{n}

. We prove that

D

n

(
x
,
a
)
+
b
∈
K
[
x
]

D_{n}(x,a)+b\in K[x]

is reducible if and only if there is a prime

p

|

n

p|n

such that

b
=
−

D

p

(
c
,

a

n

/

p

)

b=-D_{p}(c,a^{n/p})

for some

c
∈
K

c\in K

, or

n
=
4
k

n=4k

and

b
=
4

c

4

−
8

a

k

c

2

+
2

a

2
k

b=4c^{4}-8a^{k}c^{2}+2a^{2k}

for some

c
∈
K

c\in K

. This result generalizes the well-known reducibility criterion for binomials; and it provides a reducibility criterion for

T

n

(
x
)
+
c

T_{n}(x)+c

where

T

n

(
x
)

T_{n}(x)

denotes the Chebyshev polynomial of degree

n
n

.
Stieltjes moment sequences and positive definite matrix sequences
Authors: Bisgaard Torben
Published: July 2002

For a certain constant

δ
>
0

\delta >0

(a little less than

1

/

4

1/4

), every function

f
:

N

0

→
]
0
,
∞
[

f\colon \mathbb {N}_0\to ]0, \infty [

satisfying

f
(
n

)
2

≤
δ
f
(
n
−
1
)
f
(
n
+
1
)

f(n)^2\leq \delta f(n-1)f(n+1)

,

n
∈

N

n\in \mathbb {N}

, is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence

f
:

N

0

→

R

f\colon \mathbb {N}_0\to \mathbb {R}

there is a positive definite matrix sequence

(

a
n

)

(a_n)

which is not of positive type and which satisfies

tr
⁡
(

a

n
+
2

)
=
f
(
n
)

\operatorname {tr}(a_{n+2})=f(n)

,

n
∈

N

0

n\in \mathbb {N}_0

. For a certain constant

ε
>
0

\varepsilon >0

(a little greater than

1

/

6

1/6

), for every function

φ
:

N

0

→
]
0
,
∞
[

\varphi \colon \mathbb {N}_0\to ]0, \infty [

satisfying

φ
(
n

)
2

≤
ε
φ
(
n
−
1
)
φ
(
n
+
1
)

\varphi (n)^2\leq \varepsilon \varphi (n-1)\varphi (n+1)

,

n
∈

N

n\in \mathbb {N}

, there is a convolution semigroup

(

μ
t

)

t
≥
0

(\mu _t)_{t\geq 0}

of measures on

R

+

\mathbb {R}_+

, with moments of all orders, such that

φ
(
n
)
=
∫

x
n

d

μ
1

(
x
)

\varphi (n)=\int x^n\,d\mu _1(x)

,

n
∈

N

0

n\in \mathbb {N}_0

, and for every such convolution semigroup

(

μ
t

)

(\mu _t)

the measure

μ
t

\mu _t

is Stieltjes indeterminate for all

t
>
0

t>0

.
A note on the density of 𝑠-dimensional sets
Authors: Foran James
Published: July 2002

Sets in Euclidean spaces which are measurable with respect to Hausdorff

s
s

-dimensional measure with

0
>
s
>
1

0>s>1

are shown to have an at most countable set of points where the exact

s
s

-density exists and is finite and non-zero.
A topology on lattice ordered groups
Authors: Gusić Ivica
Published: July 2002

We show that a lattice ordered group can be topologized in a natural way. The topology depends on the choice of a set

C
C

of admissible elements (

C
C

-topology). If a lattice ordered group is 2-divisible and satisfies a version of Archimedes’ axiom (

C
C

-group), then we show that the

C
C

-topology is Hausdorff. Moreover, we show that a

C
C

-group with the

C
C

-topology is a topological group.
The fundamental group of a compact metric space
Authors: Pawlikowski Janusz
Published: July 2002

We give a forcing free proof of a conjecture of Mycielski that the fundamental group of a connected locally connected compact metric space is either finitely generated or has the power of the continuum.
Singular extensions of the trace and the relative Dixmier property in the type 𝐼𝐼₁ factors
Authors: Pop Florin
Published: July 2002

If

N
⊂
M

N \subset M

is an inclusion of type

I
I

1

\mathrm {II}_1

factors with

N
′

∩
M
=

C

I
,

N’\cap M = \mathbf {C} I,

we study the connection between the existence of singular states on

M
M

which extend the trace on

N
N

and the Dixmier approximation property in

M
M

with unitaries in

N
.

N.

We also prove the existence of singular conditional expectations from certain free product factors onto irreducible hyperfinite subfactors.
Van Douwen’s problem on 0-dimensional images of ordered compacta
Authors: Purisch S.
Published: July 2002

A compact 0-dimensional space has a

T
0

T_0

-separating rank 1 family of clopen sets iff it is the continuous image of a compact 0-dimensional linearly ordered space.
Evading predictors with creatures
Authors: Spinas Otmar
Published: July 2002

We continue the theory of evasion and prediction which was introduced by Blass and developed by Brendle, Shelah, and Laflamme. We prove that for arbitrary sufficiently different

f
,
g

∈

ω

ω

f,g\in ^{\omega }\omega

, it is consistent to have

e

g

>

e

f

{\mathfrak {e}}_{g}>{\mathfrak {e}}_{f}

, where

e

f

{\mathfrak {e}}_{f}

is the evasion number of the space

∏

n
>
ω

f
(
n
)

\prod _{n>\omega }f(n)

. For this we apply a variant of Shelah’s “creature forcing”.
A result on the Gelfand-Kirillov dimension of representations of classical groups
Authors: Zhu Chen-bo
Published: July 2002

Let

(
G
,

G
′

)

(G,G’)

be the reductive dual pair

(
O
(
p
,
q
)
,
S
p
(
2
n
,

R

)
)

(O(p,q),Sp(2n,\mathbb {R}))

. We show that if

π
\pi

is a representation of

S
p
(
2
n
,

R

)

Sp(2n,\mathbb {R})

(respectively

O
(
p
,
q
)

O(p,q)

) obtained from duality correspondence with some representation of

O
(
p
,
q
)

O(p,q)

(respectively

S
p
(
2
n
,

R

)

Sp(2n,\mathbb {R})

), then its Gelfand-Kirillov dimension is less than or equal to

(
p
+
q
)
(
2
n
−

p
+
q
−
1

2

)

(p+q)(2n-\frac {p+q-1}{2})

(respectively

2
n
(
p
+
q
−

2
n
+
1

2

)

2n(p+q-\frac {2n+1}{2})

).
On an example concerning the Kobayashi pseudodistance
Authors: Zwonek Włodzimierz
Published: July 2002

In this short note we calculate the Kobayashi pseudodistance for elementary Reinhardt domains in

C

2

\mathbb {C}^{2}

. They deliver us a number of examples giving a negative answer to a problem posed by S. Kobayashi.
Fixed points of the bucket handle
Authors: Aarts Jan , Fokkink Robbert
Published: July 2002

If a homeomorphism on the bucket handle has an invariant composant, it has a fixed point in that composant. It follows that a homeomorphism on the bucket handle has at least two fixed points. Our methods apply to general Knaster continua.