bluuebunny/crossref_metadata_2025 huggingface dataset:
A non-homogeneous zero-dimensional 𝑋 such that 𝑋×𝑋 is a group
Authors: van Engelen Fons
Published: July 2002

We provide an example of a zero-dimensional (separable metric) absolute Borel set

X
X

which is not homogeneous, but whose square

X
×
X

X \times X

admits the structure of a topological group. We also construct a zero-dimensional absolute Borel set

Y
Y

such that

Y
Y

is a homogeneous non-group but

Y
×
Y

Y \times Y

is a group. This answers questions of Arhangel’skiĭ and Zhou.
On the realizability of Lewy structures
Authors: Meziani Abdelhamid
Published: July 2002

We prove that a nondegenerate CR structure with signature

(
p
,
n
−
p
)

(p,n-p)

at

0
∈

R

2
n
+
1

0\in \mathbb {R}^{2n+1}

and with

n
n

first integrals

z

1

,
⋯
,

z

n

z_{1},\cdots ,z_{n}

satisfying

d

z

1

∧
d

z
¯

1

∧
⋯
∧
d

z

n

∧
d

z
¯

n

≠
0

\begin{equation*}dz_{1}\wedge d\bar {z}_{1}\wedge \cdots \wedge dz_{n}\wedge d\bar {z}_{n} \ne 0\end{equation*}

is realizable if and only if an action of the group

O
(
2
p
,
2
n
−
2
p
)

O(2p,2n-2p)

leaves invariant a one-dimensional subbundle of the structure bundle.
A submartingale inequality
Authors: Choi Changsun
Published: July 2002

This paper extends Burkholder’s inequality between a nonnegative submartingale and a process strongly differentially subordinate to it.
Sequential group topology on rationals with intermediate sequential order
Authors: Shibakov Alexander
Published: July 2002

Using CH we construct a countable sequential topological group whose sequential order is between

2
2

and

ω
\omega

giving a consistent negative answer to P. Niykos’ question.
Some remarks on Beilinson adeles
Authors: Yekutieli Amnon
Published: July 2002

Let

X
X

be a scheme of finite type over a field

k
k

. Denote by

A

X

⋅

\mathcal {A}^{{\textstyle \cdot }}_X

the sheaf of Beilinson adeles with values in the algebraic De Rham complex

Ω

X

/

k

⋅

\Omega ^{{\textstyle \cdot }}_{X/k}

. Then

Ω

X

/

k

⋅

→

A

X

⋅

\Omega ^{{\textstyle \cdot }} _{X/k}\rightarrow \mathcal {A}^{{\textstyle \cdot }}_X

is a flasque resolution. So if

X
X

is smooth,

A

X

⋅

\mathcal {A}^{{\textstyle \cdot }}_X

calculates De Rham cohomology. In this note we rewrite the proof of Deligne-Illusie for the degeneration of the Hodge spectral sequence in terms of adeles. We also give a counterexample to show that the filtration

A

X

⋅

,
≥
q

\mathcal {A}^{{\textstyle \cdot },\geq q}_X

does not induce Hodge decomposition.
Fatou theorems for parabolic equations
Authors: Sweezy Caroline
Published: July 2002

For elliptic parabolic operators with time dependent coefficients, bounded and measurable, the absolute continuity of the two caloric measures plus a Fatou theorem are shown to hold on the parabolic boundary of a smooth cylinder given a Carleson-type condition on the coefficients of the operators, and assuming one of the measures is a center doubling measure. Given a stronger Carleson condition, and no doubling assumption, another kind of Fatou theorem result holds. The method of proof follows that of Fefferman, Kenig and Pipher.
Commuting holomorphic functions and hyperbolic automorphisms
Authors: de Fabritiis Chiara
Published: July 2002

We give a complete classification of the holomorphic self-maps of the unit ball of

C

n

\mathbf {C}^{n}

into itself which commute with a given hyperbolic automorphism.
Théorème de l’application spectrale pour le spectre essentiel quasi-Fredholm
Authors: Berkani M. , Ouahab A.
Published: July 2002

In 1958, T. Kato proved that a closed semi-Fredholm operator

A
A

in a Banach space can be written

A
=

A
1

⊕

A
0

A=A_1\oplus A_0

where

A
0

A_0

is a nilpotent operator and

A
1

A_1

is a regular one. J. P. Labrousse studied and characterised this class of operators in the case of Hilbert spaces. He also defined a new spectrum named “essential quasi-Fredholm spectrum” and denoted

σ
e

(
A
)

\sigma _e(A)

. In this paper we prove that the essential quasi-Fredholm spectrum defined by J. P. Labrousse satisfies the mapping spectral theorem, i.e.: If

A
A

is a bounded operator in a Hilbert space and

f
f

an analytic function in a neighbourhood of the spectrum

σ
(
A
)

\sigma (A)

of

A
A

, then

f
(

σ
e

(
A
)
)
=

σ
e

(
f
(
A
)
)

f(\sigma _e(A)) =\sigma _e(f(A))

.

Résumé. En 1958, T. Kato a montré que si

A
A

est un opérateur fermé dans un espace de Banach et semi-Fredholm, alors il existe

A
1

,

A
0

A_1,A_0

tels que

A
=

A
1

⊕

A
0

A=A_1\oplus A_0

où

A
0

A_0

est nilpotent et

A
1

A_1

est régulier. J. P. Labrousse a étudié et caractérisé cette classe d’opérateurs dans le cadre des espaces de Hilbert et a défini un nouveau spectre qu’on appelle “spectre essentiel quasi-Fredholm” et noté par

σ
e

(
A
)

\sigma _e(A)

. Dans ce travail nous allons démontrer que le spectre essentiel quasi-Fred- holm défini par J. P. Labrousse vérifie le théorème de l’application spectrale, c’est à dire: Si

A
A

est un opérateur bourné d’un espace de Hilbert dans lui même et

f
f

une fonction analytique au voisinage du spectre

σ
(
A
)

\sigma (A)

de

A
A

, alors

f
(

σ
e

(
A
)
)
=

σ
e

(
f
(
A
)
)

f(\sigma _e(A))=\sigma _e(f(A))

.
A family of new universal 𝑅-matrices
Authors: Liu Keqin
Published: July 2002

Left universal

R
R

–matrices and right universal

R
R

–matrices are introduced. A family of new universal

R
R

–matrices and charmed Hopf algebra is found.
A note on the path holomorphy of random functions holomorphic in mean
Authors: Martinez F. , Villena A.
Published: July 2002

Every random function holomorphic in mean on an open subset of the complex field is equivalent to a random function with almost all its paths holomorphic on

D
D

.
Height of flat tori
Authors: Chiu Patrick
Published: July 2002

Relations between the height and the determinant of the Laplacian on the space of

n
n

-dimensional flat tori and the classical formulas of Kronecker and Epstein are established. Extrema of the height are shown to exist, and results for a global minimum for 2-d tori and a local minimum for 3-d tori are given, along with more general conjectures of Sarnak and Rankin.
Applications of residues to combinatorial identities
Authors: Huang I-Chiau
Published: July 2002

A concrete aspect of Grothendieck Duality is used to give local cohomology proofs of combinatorial identities including MacMahon’s master theorem, Grosswald identity, identity of Shoo, Tepper identity, and others.
Weakly convergent sequence coefficient in Köthe sequence spaces
Authors: Cui Yunan
Published: July 2002

In this paper, we have discussed the weakly convergent sequence coefficient in Köthe sequence spaces with

(

e
n

)

(e_n)

as their boundedly complete basis. Using those results, we can easily calculate the weakly convergent sequence coefficient in Orlicz sequence spaces.
Distinguishing embedded curves in rational complex surfaces
Authors: Fuller Terry
Published: July 2002

We construct many pairs of smoothly embedded complex curves with the same genus and self-intersection number in the rational complex surfaces

C

P

2

#
n

C

P

¯

2

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

with the property that no self-diffeomorphism of

C

P

2

#
n

C

P

¯

2

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

sends one to the other. In particular, as a special case we answer a question originally posed by R. Gompf (1995) concerning genus two curves of self-intersection number 0 in

C

P

2

#
13

C

P

¯

2

\mathbb {C} P^{2} \# 13\overline {\mathbb {C} P}^{2}

.
The Schrödinger operator
Authors: Lixin Tian , Zengrong Liu
Published: July 2002

In this paper we study the maximum dissipative extension of the Schrödinger operator, introduce the generalized indefinite metric space, obtain the representation of the maximum dissipative extension of the Schrödinger operator in the natural boundary space and make preparation for the further study of the longtime chaotic behavior of the infinite-dimensional dynamics system in the Schrödinger equation.
Lifting up an infinite chain of prime ideals to a valuation ring
Authors: Kang Byung , Oh Dong
Published: July 2002

We prove that for an arbitrary chain

{

P
α

}

\{P_\alpha \}

of prime ideals in an integral domain, there exists a valuation domain which has a chain of prime ideals

{

Q
α

}

\{Q_\alpha \}

lying over

{

P
α

}

\{P_\alpha \}

.
On the infinite product of operators in Hilbert space
Authors: Mate László
Published: July 2002

We give a necessary and sufficient condition for a certain set of infinite products of linear operators to be zero. We shall investigate also the case when this set of infinite products converges to a non-zero operator. The main device in these results is a weighted version of the König Lemma for infinite trees in graph theory.
Order-topological separable complete modular ortholattices admit order continuous faithful valuations
Authors: Riečanová Zdenka
Published: July 2002

We prove that on every separable complete atomic modular ortholattice (i.e. order topological) there exists an order continuous faithful valuation. We also give a construction of the existing order continuous faithful valuation. For separable atomic modular ortholattices we give a necessary and sufficient condition to admit an order continuous faithful valuation and we show that it is equivalent with the condition to have a modular MacNeille completion. We improve one statement on complete metric lattices from Birkhoff’s Lattice Theory.
A counterexample to a 𝐵𝑃-analogue of the chromatic splitting conjecture
Authors: Devinatz Ethan
Published: July 2002

We prove that, if

n
≥
2

n\ge 2

, the

E
(
n
−
1

)
∗

E(n-1)_\ast

-localization of the

K
(
n

)
∗

K(n)_\ast

-localization map

B

P
p

→

L

K
(
n
)

B
P

BP_p\to L_{K(n)}BP

is not a split monomorphism in the stable category by exhibiting spectra

Z
Z

for which the map
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi Subscript asterisk Baseline left-parenthesis upper L Subscript n minus 1 Baseline left-parenthesis upper B upper P Subscript p Baseline right-parenthesis logical-and upper Z right-parenthesis right-arrow pi Subscript asterisk Baseline left-parenthesis upper L Subscript n minus 1 Baseline left-parenthesis upper L Subscript upper K left-parenthesis n right-parenthesis Baseline upper B upper P right-parenthesis logical-and upper Z right-parenthesis">

π
∗

(

L

n
−
1

(
B

P
p

)
∧
Z
)
→

π
∗

(

L

n
−
1

(

L

K
(
n
)

B
P
)
∧
Z
)

\pi _\ast (L_{n-1}(BP_p)\wedge Z)\to \pi _\ast (L_{n-1}(L_{K(n)}BP)\wedge Z)

is not injective. If

p
≥
max
{

1
2

(

n
2

−
2
n
+
2
)
,
n
+
1
}

p\ge \max \{\frac {1}{2}(n^2-2n +2), n+1\}

and

n
≥
3

n\geq 3

, we show that

Z
Z

may be taken to be a two-cell complex in the sense of

E
(
n
−
1

)
∗

E(n-1)_\ast

-local homotopy theory. The question of whether the map
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Subscript n minus 1 Baseline left-parenthesis upper B upper P Subscript p Baseline right-parenthesis right-arrow upper L Subscript n minus 1 Baseline upper L Subscript upper K left-parenthesis n right-parenthesis Baseline upper B upper P">

L

n
−
1

(
B

P
p

)
→

L

n
−
1

L

K
(
n
)

B
P

L_{n-1}(BP_p)\to L_{n-1}L_{K(n)}BP

splits was asked by Hovey and is in some sense a

B
P

BP

-analogue of Hopkins’ chromatic splitting conjecture.
On the jacobian module associated to a graph
Authors: Simis Aron
Published: July 2002

We consider the jacobian module of a set

f

:=
{

f
1

,
…
,

f
m

}
∈
R
:=
k
[

X
1

,
…
,

X
n

]

\mathbf {f}:=\{f_1,\ldots ,f_m\} \in R:=k[X_1,\ldots ,X_n]

of squarefree monomials of degree

2
2

corresponding to the edges of a connected bipartite graph

G
G

. We show that for such a graph

G
G

the number of its primitive cycles (i.e., cycles whose chords are not edges of

G
G

) is the second Betti number in a minimal resolution of the corresponding jacobian module. A byproduct is a graph theoretic criterion for the subalgebra

k
[
G
]
:=
k
[

f

]

k[G]:=k[\mathbf {f}]

to be a complete intersection.
A Banach couple is determined by the collection of its interpolation spaces
Authors: Tikhonov O. , Veselova L.
Published: July 2002

We prove that an arbitrary Banach couple is uniquely determined by the collection of all its interpolation spaces, which extends a result by N. Aronszajn and E. Gagliardo.
On solvability of second-order Sturm-Liouville boundary value problems at resonance
Authors: Yujun Dong
Published: July 2002

In this paper, based on of the concept

q
0

∈

H
0

(
p
,
(
0
,
1
)
,
α
,
β
)

q_0\in H_0(p,(0,1),\alpha ,\beta )

, which is a generalized form of the first resonant point

π
2

\pi ^2

to the Picard problem

x
+
λ
x
=
0

x+\lambda x=0

,

x
(
0
)
=
x
(
1
)
=
0

x(0)=x(1)=0

, we study the solvability of second-order Sturm-Liouville boundary value problems at resonance

(
p
(
t
)

x
′

)
′

+

q
0

(
t
)
x
+
g
(
t
,
x
)
=
h
(
t
)

(p(t)x’)’+q_0(t)x+g(t,x)=h(t)

,

x
(
0
)

cos
⁡
α

−
p
(
0
)

x
′

(
0
)
sin
⁡
α
=
0

x(0){\cos \alpha }-p(0)x’(0)\sin \alpha =0

,

x
(
1
)
cos
⁡
β
−
p
(
1
)

x
′

(
1
)
sin
⁡
β
=
0

x(1)\cos \beta -p(1)x’(1)\sin \beta =0

, and improve the previous results about problems

x
+

π
2

x
+
g
(
t
,
x
)
=
h
(
t
)
,
x
(
0
)
=
x
(
1
)
=
0

x+\pi ^2x+g(t,x)=h(t),x(0)=x(1)=0

derived by Chaitan P. Gupta, R. Iannacci and M. N. Nkashama, and Ma Ruyun, respectively.
Maximal nests in the Calkin algebra
Authors: Hadwin Don
Published: July 2002

We prove that if two countable commutative lattices of projections in the Calkin algebra are order isomorphic, then they are unitarily equivalent. We show that there are isomorphic maximal nests of projections in the Calkin algebra that are order isomorphic but not similar. Assuming the continuum hypothesis, we show that all maximal nests of projections in the Calkin algebra are order isomorphic.
On an isomorphism problem for endomorphism near-rings
Authors: Peterson Gary
Published: July 2002

Suppose

R
R

and

S
S

are endomorphism near-rings generated by groups of automorphisms containing the inner automorphisms of two respective finite perfect groups

G
G

and

H
H

. In this note we show that if

R
R

and

S
S

are isomorphic, then

G

/

Z
(
G
)

G/Z(G)

and

H

/

Z
(
H
)

H/Z(H)

are isomorphic.
Relative to any nonrecursive set
Authors: Slaman Theodore
Published: July 2002

There is a countable first order structure

M

\mathcal {M}

such that for any set of integers

X
X

,

X
X

is not recursive if and only if there is a presentation of

M

\mathcal {M}

which is recursive in

X
X

.
Linear operators that preserve maximal column ranks of nonnegative integer matrices
Authors: Song Seok-zun
Published: July 2002

The maximal column rank of an

m
m

by

n
n

matrix over a semiring is the maximal number of the columns of

A
A

which are linearly independent. We characterize the linear operators which preserve the maximal column ranks of nonnegative integer matrices.
Ordinary differential inequalities and quasimonotonicity in ordered topological vector spaces
Authors: Uhl Roland
Published: July 2002

A well known comparison theorem on ordinary differential inequalities with quasimonotone right-hand side

f
(
t
,
x
)

f(t,x)

was carried over by Volkmann (1972) to (pre)ordered topological vector spaces. We prove that the quasimonotonicity of

f
f

is a necessary condition here if

f
f

is continuous. Then it is shown that quasimonotonicity can be verified by considering only a few positive continuous linear functionals in the definition (for instance in

ℓ

∞

\ell _{\infty }

by taking coordinate functionals).
Spectral properties of the operator of Riesz potential type
Authors: Dostanić Milutin
Published: July 2002

For the operator of the Riesz potential type we estimate the second term in the asymptotic behavior of the spectrum and find its “regularized” trace.
Some results on finite Drinfeld modules
Authors: Hsu Chih-Nung
Published: July 2002

Let

K
\operatorname {K}

be a global function field,

∞
\infty

a degree one prime divisor of

K
\operatorname {K}

and let

A
\operatorname {A}

be the Dedekind domain of functions in

K
\operatorname {K}

regular outside

∞
\infty

. Let

H
\operatorname {H}

be the Hilbert class field of

A
\operatorname {A}

,

B
\operatorname {B}

the integral closure of

A
\operatorname {A}

in

H
\operatorname {H}

. Let

ψ
\psi

be a rank one normalized Drinfeld

A
\operatorname {A}

-module and let

P

\mathfrak P

be a prime ideal in

B
\operatorname {B}

. We explicitly determine the finite

A
\operatorname {A}

-module structure of

ψ
(
B
⁡

/

P

N

)

\psi (\operatorname {B} /\mathfrak P^N)

. In particular, if

K
=

F

q

(
t
)

\operatorname {K} =\mathbb F_q(t)

,

q
q

is an odd prime number and

ψ
\psi

is the Carlitz

F

q

[
t
]

\mathbb F_q[t]

-module, then the finite

F

q

[
t
]

\mathbb F_q[t]

-module

ψ
(

F

q

[
t
]

/

P

N

)

\psi (\mathbb F_q[t]/\mathfrak P^N)

is always cyclic.
Linear constituents of certain character restrictions
Authors: Isaacs I. , Robinson G.
Published: July 2002

Let

G
G

be a finite irreducible complex linear group with

p
p

-power degree, where

p
p

is a prime number. Then every

p
′

p’

-subgroup of

G
G

that is normalized by a Sylow

p
p

-subgroup must be abelian. This and related results are proved using an elementary character-theoretic argument.
On reductive group actions and fixed points
Authors: Kim Minhyong
Published: July 2002

Among analytic actions of reductive groups on projective varieties, we characterize the algebraic ones by the existence of fixed points for one-parameter subgroups. This applies to the problem of lifting the action of a compact Lie group on a projective manifold to a line bundle.
New fixed point theorems for a family of mappings and applications to problems on sets with convex sections
Authors: Lan Kunquan , Webb Jeffrey
Published: July 2002

Some new fixed point theorems for a family of mappings are obtained and applied to problems on sets with convex sections that were first studied by Ky Fan.
Microlocal analysis of ultradistributions
Authors: Pilipović Stevan
Published: July 2002

The ultradistributional wave front sets of an ultradistribution

u
u

are characterized by the behaviour of

K
∗
u

K *u

on the boundary of the tube domain

D

R

n

D \mathbf {R}^n

, where

K
K

is the kernel analysed by Hörmander.
On a conjecture of F. Móricz
Authors: Brown G. , Wang K.
Published: July 2002

F. Móricz has investigated the integrability of double lacunary sine series. His result, valid for special lacunary sequences, does not extend in the form originally conjectured, but we establish a suitably modified result.
Subsystems of the Schauder system that are quasibases for 𝐿^{𝑝}[0,1],1≤𝑝<+∞
Authors: Kazarian K. , Zink Robert
Published: July 2002

We show that if

Φ
=
{

φ
i

:
i
=
1
,
2
,
…
}

\Phi =\{\varphi _i\colon i=1,2,\ldots \}

is a subsystem of the Faber-Schauder system, and if

Φ
\Phi

is complete in

L
2

[
0
,
1
]

L^2[0,1]

, then

Φ
\Phi

is a quasibasis for each space

L
p

[
0
,
1
]

L^p[0,1]

,

1
≤
p
>
+
∞

1\le p>+\infty

. Although it follows from the work of Ul’yanov that each element of

L
p

[
0
,
1
]

L^p[0,1]

can be represented by a Schauder series that converges unconditionally to the function, in the metric of the space, it proves to be the case that none of the aforementioned systems is an unconditional quasibasis for any of the

L
p

L^p

-spaces herein considered.
Derivations implemented by local multipliers
Authors: Mathieu Martin
Published: July 2002

A condition on a derivation of an arbitrary C*-algebra is presented entailing that it is implemented as an inner derivation by a local multiplier.
Glasner sets and polynomials in primes
Authors: Nair R. , Velani S.
Published: July 2002

A set of integers

S
S

is said to be Glasner if for every infinite subset

A
A

of the torus

T

=

R

/

Z

\mathbb {T}=\mathbb {R}/\mathbb {Z}

and

ε
>
0

\varepsilon >0

there exists some

n
∈
S

n\in S

such that the dilation

n
A
=
{
n
x
:
x
∈
A
}

nA=\{nx\colon x\in A\}

intersects every integral of length

ε
\varepsilon

in

T

\mathbb {T}

. In this paper we show that if

p
n

p_n

denotes the

n
n

th prime integer and

f
f

is any non-constant polynomial mapping the natural numbers to themselves, then

(
f
(

p
n

)

)

n
≥
1

(f(p_n))_{n\geq 1}

is Glasner. The theorem is proved in a quantitative form and generalizes a result of Alon and Peres (1992).
Centroaffine surfaces in ℝ⁴ with planar ∇-geodesics
Authors: Scharlach Christine , Vrancken Luc
Published: July 2002

For (positive) definite surfaces in

R

4

\mathbb {R}^{4}

there is a canonical choice of a centroaffine normal plane bundle, which induces a centroaffine invariant Ricci-symmetric connection

∇
\nabla

. We classify all surfaces in

R

4

\mathbb {R}^{4}

with planar

∇
\nabla

-geodesics. It turns out that the resulting class of surfaces is umbilical with projectively flat induced connection and flat normal plane bundle.
Cohomology of polynomials under an irrational rotation
Authors: Baggett Lawrence , Medina Herbert , Merrill Kathy
Published: July 2002

A new description of cohomology of functions under an irrational rotation is given in terms of symmetry properties of the functions on subintervals of

[
0
,
1
]
.

[0,1].

This description yields a method for passing information about the cohomology classes for a given irrational to the cohomology classes for an equivalent irrational.
A pointwise spectrum and representation of operators
Authors: Bertoglio N. , Martínez Servet , Martín Jaime
Published: July 2002

For a self-adjoint operator

A
:
H
→
H

A:H\to H

commuting with an increasing family of projections

P

=
(

P

t

)

{\mathcal {P}}=(P_{t})

we study the multifunction

t
→

Γ

T

(
t
)
=
⋂
{

σ

I

:
I

t\to \Gamma ^{\mathcal {T}}(t)=\bigcap \{\sigma _{I}:I

an open set of the topology

T

{\mathcal {T}}

containing

t
}

t\}

, where

σ

I

\sigma _{I}

is the spectrum of

A
A

on

P

I

H

P_{I}H

. Let

m

P

m_{\mathcal {P}}

be the measure of maximal spectral type. We study the condition that

Γ

T

\Gamma ^{\mathcal {T}}

is essentially a singleton,

m

P

{
t
:

Γ

T

(
t
)

m_{\mathcal {P}}\{t:\Gamma ^{\mathcal {T}}(t)

is not a singleton

}
=
0

\}=0

. We show that if

T

{\mathcal {T}}

is the density topology and if

m

P

m_{\mathcal {P}}

satisfies the density theorem, in particular if it is absolutely continuous with respect to the Lebesgue measure, then this condition is equivalent to the fact that

A
A

is a Borel function of

P

{\mathcal {P}}

. If

T

{\mathcal {T}}

is the usual topology then the condition is equivalent to the fact that

A
A

is approched in norm by step functions
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript n element-of double-struck upper N Endscripts normal upper Gamma Superscript script upper T Baseline left-parenthesis alpha Subscript n Baseline right-parenthesis mathematical left-angle upper P Subscript upper I Sub Subscript n Subscript Baseline f comma f mathematical right-angle">

∑

n
∈

N

Γ

T

(

α

n

)
⟨

P

I

n

f
,
f
⟩

\sum \limits _{n\in \mathbb {N}}\Gamma ^{\mathcal {T}} (\alpha _{n})\langle P_{I_{n}} f,f\rangle

, where the set of intervals

{

I

n

:
n
∈

N

}

\{I_{n}:n\in \mathbb {N}\}

covers the set where

Γ

T

\Gamma ^{\mathcal {T}}

is a singleton.
Extending the formula to calculate the spectral radius of an operator
Authors: Bonales Fernando , Mendoza Rigoberto
Published: July 2002

In a Banach space, Gelfand’s formula is used to find the spectral radius of a continuous linear operator. In this paper, we show another way to find the spectral radius of a bounded linear operator in a complete topological linear space. We also show that Gelfand’s formula holds in a more general setting if we generalize the definition of the norm for a bounded linear operator.
Algebraic cuts
Authors: Edidin Dan , Graham William
Published: July 2002

In this note we give an algebraic version of a construction called symplectic cutting, which is due to Lerman. Our construction is valid for projective varieties defined over arbitrary fields. Using the equivariant intersection theory developed by the authors, it is a useful tool for studying quotients by torus actions. At the end of the paper, we give an algebraic proof of the Kalkman residue formula and use it to give some formulas for characteristic numbers of quotients.
Algebraic lattices and nonassociative structures
Authors: López Antonio , Rus Eulalia
Published: July 2002

Uniform elements in algebraic lattices are studied and their relationship with some nonassociative extensions of Goldie’s Second Theorem is shown.
Groups acting on cubes and Kazhdan’s property (T)
Authors: Niblo Graham , Roller Martin
Published: July 2002

We show that a group

G
G

contains a subgroup

K
K

with

e
(
G
,
K
)
>
1

e(G,K) > 1

if and only if it admits an action on a connected cube that is transitive on the hyperplanes and has no fixed point. As a corollary we deduce that a countable group

G
G

with such a subgroup does not satisfy Kazhdan’s property (T).
A theorem on iterations of polynomial maps in several variables
Authors: Bernardes Nilson
Published: July 2002

We establish a polynomial version of a theorem obtained by Enflo, Gurarii, Lomonosov and Lyubich for linear operators. As a consequence, we also derive a polynomial version of a result due to Pták.
On the cohomology of regular differential forms and dualizing sheaves
Authors: Hübl Reinhold , Sun Xiaotao
Published: July 2002

If

Y
Y

is a local Dedekind scheme and

X

/

Y

X/Y

is a projective Cohen–Macaulay variety of relative dimension

1
1

, then

R

1

f

∗

ω

X

/

Y

1

R^{1} f_{*} \omega ^{1}_{X/Y}

is torsionfree if and only if

X

/

Y

X/Y

is arithmetically Cohen–Macaulay for a suitable embedding in

P

k

n

\mathbb {P}^{n}_{k}

. If

X
X

is regular then

R

1

f

∗

ω

X

/

Y

1

R^{1} f_{*} \omega ^{1}_{X/Y}

is torsionfree whenever the multiplicity of the special fibre is not a multiple of the characteristic of the residue class field.
Boundedness of the Cesàro operator on mixed norm spaces
Authors: Shi Ji-huai , Ren Guang-bin
Published: July 2002

In this note, the boundedness of the Cesàro operator on mixed norm space

H

p
,
q

(
φ
)

H_{p,q}(\varphi )

,

0
>
p
,
q
≤
∞

0>p, q\le \infty

, is proved.
Banach spaces failing the almost isometric universal extension property
Authors: Speegle D.
Published: July 2002

If

X
X

is an infinite dimensional, separable, uniformly smooth Banach space, then there is an

ϵ
>
0

\epsilon > 0

, a Banach space

Y
Y

containing

X
X

as a closed subspace and a norm one map

T
T

from

X
X

to a

C
(
K
)

C(K)

space which does not extend to an operator

T
~

\tilde T

from

Y
Y

to

C
(
K
)

C(K)

with

‖

T
~

‖
≤
1
+
ϵ

\|\tilde T\| \le 1+\epsilon

.
On complementary subspaces of Hilbert space
Authors: Longstaff W. , Panaia Oreste
Published: July 2002

Every pair

{
M
,
N
}

\{M,N\}

of non-trivial topologically complementary subspaces of a Hilbert space is unitarily equivalent to a pair of the form

{
G
(
−
A
)
⊕
K
,
G
(
A
)
⊕
(
0
)
}

\left \{G(-A)\oplus K,G(A)\oplus (0)\right \}

on a Hilbert space

H
⊕
H
⊕
K

H\oplus H\oplus K

. Here

K
K

is possibly

(
0
)

(0)

,

A
∈

B

(
H
)

A\in \mathcal {B}(H)

is a positive injective contraction and

G
(
±
A
)

G(\pm A)

denotes the graph of

±
A

\pm A

. For such a pair

{
M
,
N
}

\{M,N\}

the following are equivalent: (i)

{
M
,
N
}

\{M,N\}

is similar to a pair in generic position; (ii)

M
M

and

N
N

have a common algebraic complement; (iii)

{
M
,
N
}

\{M,N\}

is similar to

{
G
(
X
)
,
G
(
Y
)
}

\left \{G(X),G(Y)\right \}

for some operators

X
,
Y

X,Y

on a Hilbert space. These conditions need not be satisfied. A second example is given (the first due to T. Kato), involving only compact operators, of a double triangle subspace lattice which is not similar to any operator double triangle.
𝑀-ideals of compact operators are separably determined
Authors: Oja Eve
Published: July 2002

We prove that the space

K
(
X
)

K(X)

of compact operators on a Banach space

X
X

is an

M
M

-ideal in the space

L
(
X
)

L(X)

of bounded operators if and only if

X
X

has the metric compact approximation property (MCAP), and

K
(
Y
)

K(Y)

is an

M
M

-ideal in

L
(
Y
)

L(Y)

for all separable subspaces

Y
Y

of

X
X

having the MCAP. It follows that the Kalton-Werner theorem characterizing

M
M

-ideals of compact operators on separable Banach spaces is also valid for non-separable spaces: for a Banach space

X
,
K
(
X
)

X, K(X)

is an

M
M

-ideal in

L
(
X
)

L(X)

if and only if

X
X

has the MCAP, contains no subspace isomorphic to

ℓ

1

,

\ell _{1},

and has property

(
M
)
.

(M).

It also follows that

K
(
Z
,
X
)

K(Z,X)

is an

M
M

-ideal in

L
(
Z
,
X
)

L(Z,X)

for all Banach spaces

Z
Z

if and only if

X
X

has the MCAP, and

K
(

ℓ

1

,
X
)

K(\ell _{1},X)

is an

M
M

-ideal in

L
(

ℓ

1

,
X
)

L(\ell _{1},X)

.
A note on invariance of spectrum for symmetric Banach *-algebras
Authors: Barnes Bruce
Published: July 2002

Let

A
A

be a symmetric Banach

∗

^*

-algebra, let

B
B

be a Banach algebra, and assume that

A
⊆
B

A\subseteq B

. A result is proved giving conditions which imply that every element of

A
A

has the same spectrum in both

A
A

and

B
B

.
A volume comparison theorem for Finsler manifolds
Authors: Durán Carlos
Published: July 2002

Let

(

M

n

,
F
)

(M^{n},F)

be a symmetric Finsler manifold, endowed with the Busemann volume form, and let

D
D

be its unit disk bundle endowed with the canonical symplectic volume form. It is shown that

V
o
l
(
D
)
≤
C
(
n
)
V
o
l
(

M

n

)

Vol(D)\leq C(n)Vol(M^{n})

, where

C
(
n
)

C(n)

is the volume of the unit disk in

R

n

{\mathbb {R}}^{n}

. Moreover, equality holds if and only if

(

M

n

,
F
)

(M^{n},F)

is Riemannian.
A Leray-Schauder type theorem for approximable maps: A simple proof
Authors: Ben-El-Mechaiekh H. , Chebbi S. , Florenzano M.
Published: July 2002

We present a simple and direct proof for a Leray-Schauder type alternative for a large class of condensing or compact set-valued maps containing convex as well as nonconvex maps.
A note on the Gelfand-Mazur Theorem
Authors: Bhatt S. , Karia D. , Kulkarni S. , Shimpi M.
Published: July 2002

Three Gelfand-Mazur type theorems are proved. One of these provides a

C
∗

C^*

-property analogue of Zalar’s recent generalizations of the Froelich-Ingelstam-Smiley Theorems concerning unital multiplication in Hilbert spaces; the second illustrates that the assumption in Kaplansky’s version of the Gelfand-Mazur Theorem can be weakened in the presence of a

C
∗

C^*

-norm; whereas the third provides a real analogue of a result due to Srinivasan.
On subwavelet sets
Authors: Ionascu Eugen , Pearcy Carl
Published: July 2002

In this note we give a characterization of subwavelet sets and show that any point

x
∈

R

∖

0

x\in \mathbb {R}\setminus {0}

has a neighborhood which is contained in a regularized wavelet set.
Triangular extension spectrum of weighted shifts
Authors: Pan Zhidong
Published: July 2002

A necessary and sufficient condition for a complex number to be in the triangular extension spectrum of a weighted backward shift is obtained. It is shown that the triangular extension spectrum of a weighted backward shift is always a closed annulus when it is not empty. Moreover, for any given closed annulus, there exists a weighted backward shift with the annulus as its triangular extension spectrum.
A uniform boundedness theorem for locally convex cones
Authors: Roth Walter
Published: July 2002

We prove a uniform boundedness theorem for families of linear operators on ordered cones. Using the concept of locally convex cones we introduce the notions of barreled cones and of weak cone-completeness. Our main result, though no straightforward generalization of the classical case, implies the Uniform Boundedness Theorem for Fréchet spaces.
Uniqueness in the Cauchy problems for higher order elliptic differential operators
Authors: Wang Wensheng
Published: July 2002

In this note, we study the uniqueness in Cauchy problems for a class of higher order elliptic differential operators with Lipschitz coefficients. In particular, we prove the uniqueness under assuming the potentials being

L

loc

r

j

L^{r_{j}}_{ \text {loc}}

with certain correct numbers

r

j

r_{j}

’s.
𝑄𝑞𝑝𝑖 groups and quasi-equivalence
Authors: Goeters H. , Wickless W.
Published: July 2002

A torsion-free abelian group

G
G

is

q
p
i

qpi

if every map from a pure subgroup

K
K

of

G
G

into

G
G

lifts to an endomorphism of

G
.

G.

The class of

q
p
i

qpi

groups has been extensively studied, resulting in a number of nice characterizations. We obtain some characterizations for the class of homogeneous

Q
q
p
i

Qqpi

groups, those homogeneous groups

G
G

such that, for

K
K

pure in

G
,

G,

every

θ
:
K
→
G

\theta :K\rightarrow G

has a lifting to a quasi-endomorphism of

G
.

G.

An irreducible group is

Q
q
p
i

Qqpi

if and only if every pure subgroup of each of its strongly indecomposable quasi-summands is strongly indecomposable. A

Q
q
p
i

Qqpi

group

G
G

is

q
p
i

qpi

if and only if every endomorphism of

G
G

is an integral multiple of an automorphism. A group

G
G

has minimal test for quasi-equivalence (

m
t
q
e
)

mtqe)

if whenever

K
K

and

L
L

are quasi-isomorphic pure subgroups of

G
G

then

K
K

and

L
L

are equivalent via a quasi-automorphism of

G
.

G.

For homogeneous groups, we show that in almost all cases the

Q
q
p
i

Qqpi

and

m
t
q
e

mtqe

properties coincide.
Uniform primeness of the Jordan algebra of symmetric operators
Authors: Stachó L. , Zalar B.
Published: July 2002

In this note we establish the best possible constant for the general lower estimate for the Jacobson - McCrimmon operator on the algebra of symmetric operators acting on a Hilbert space.
Quasinormal subrelations of ergodic equivalence relations
Authors: Danilenko Alexandre
Published: July 2002

We introduce a notion of quasinormality for a nested pair

S

⊂

R

\mathcal {S}\subset \mathcal {R}

of ergodic discrete hyperfinite equivalence relations of type

I

I

1

II_{1}

. (This is a natural extension of the normality concept due to Feldman-Sutherland-Zimmer.) Such pairs are characterized by an irreducible pair

F
⊂
Q

F\subset Q

of countable amenable groups or rather (some special) their Polish closure

F
¯

⊂

Q
¯

\overline {F}\subset \overline {Q}

. We show that “most” of the ergodic subrelations of

R

\mathcal {R}

are quasinormal and classify them. An example of a nonquasinormal subrelation is given. We prove as an auxiliary statement that two cocycles of

R

\mathcal {R}

with dense ranges in a Polish group are weakly equivalent.
Linear maps preserving the isomorphism class of lattices of invariant subspaces
Authors: Jafarian Ali , Rodman Leiba , Šemrl Peter
Published: July 2002

Let

V

{\mathcal {V}}

be an

n
n

-dimensional complex linear space and

L

(

V

)

{\mathcal {L}}({\mathcal {V}})

the algebra of all linear transformations on

V

{\mathcal {V}}

. We prove that every linear map on

L

(

V

)

{\mathcal {L}}({\mathcal {V}})

, which maps every operator into an operator with isomorphic lattice of invariant subspaces, is an inner automorphism or an inner antiautomorphism multiplied by a nonzero constant and additively perturbed by a scalar type operator. The same result holds if we replace the lattice of invariant subspaces by the lattice of hyperinvariant subspaces or the set of reducing subspaces. Some of these results are extended to linear transformations of finite-dimensional linear spaces over fields other than the complex numbers. We also characterize linear bijective maps on the algebra of linear bounded operators on an infinite-dimensional complex Hilbert space which have similar properties with respect to the lattice of all invariant subpaces (not necessarily closed).
Cycle rank of Lyapunov graphs and the genera of manifolds
Authors: Cruz R. , de Rezende K.
Published: July 2002

We show that the cycle-rank

r
(
L
)

r(L)

of a Lyapunov graph

L
L

on a manifold

M
M

satisfies:

r
(
L
)
≤
g
(
M
)

r(L) \leq g(M)

, where

g
(
M
)

g(M)

is the genus of

M
M

. This generalizes a theorem of Franks. We also show that given any integer

r
r

with

0
≤
r
≤
g
(
M
)

0 \leq r \leq g(M)

,

r
=
r
(
L
)

r = r(L)

for some Lyapunov graph

L
L

on

M
,
dim
⁡
M
>
2

M, \dim M > 2

.
A rational invariant for knot crossings
Authors: Lee Youn
Published: July 2002

A rational number-valued invariant is constructed for the crossings of knot projections. The invariant completely determines the signature and (signed) determinant of the knot obtained by changing the crossing. In particular, if the invariant is not 0, then the new knot is distinct from the old one.
Algebras of invariant functions on the Shilov boundaries of Siegel domains
Authors: Dooley Anthony , Zhang Genkai
Published: July 2002

Let

D
=
G

/

K

D=G/K

be a bounded symmetric domain and

K

/

L

K/L

the Shilov boundary of

D
D

. Let

N

\mathcal {N}

be the Shilov boundary of the Siegel domain realization of

G

/

K

G/K

. We consider the case when

D
D

is the exceptional non-tube type domain of the type

(

e

6
(
−
14
)

,

s
o

(
10
)
×

s
o

(
2
)
)

(\mathfrak {e}_{6(-14)}, \mathfrak {so}(10)\times \mathfrak {so}(2))

. We prove that

(

N

⋊
L
,
L
)

(\mathcal {N}\rtimes L, L)

is not a Gelfand pair and thus resolve an open question of G. Carcano.
Symmetries of Accola-Maclachlan and Kulkarni surfaces
Authors: Broughton S. , Bujalance E. , Costa A. , Gamboa J. , Gromadzki G.
Published: July 2002

For all

g
≥
2

g \ge 2

there is a Riemann surface of genus

g
g

whose automorphism group has order

8
g
+
8

8g+8

, establishing a lower bound for the possible orders of automorphism groups of Riemann surfaces. Accola and Maclachlan established the existence of such surfaces; we shall call them Accola-Maclachlan surfaces. Later Kulkarni proved that for sufficiently large

g
g

the Accola-Maclachlan surface was unique for

g
=
0
,
1
,
2

mod

4

g= 0,1,2\mod 4

and produced exactly one additional surface (the Kulkarni surface) for

g
=
3

mod

4

g= 3\mod 4

. In this paper we determine the symmetries of these special surfaces, computing the number of ovals and the separability of the symmetries. The results are then applied to classify the real forms of these complex algebraic curves. Explicit equations of these real forms of Accola-Maclachlan surfaces are given in all but one case.
A new characterization of 𝑃𝑟𝑜𝑗¹𝒳=0 for countable spectra of (LB)-spaces
Authors: Wengenroth Jochen
Published: July 2002

The derived projective limit functor Proj

1

^1

is a very useful tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations). We provide a new characterization for vanishing Proj

1

^1

on projective spectra of (LB)-spaces which improves a classical result of V. P. Palamodov and V. S. Retakh.
On subspaces of pseudoradial spaces
Authors: Dow Alan , Zhou Jinyuan
Published: July 2002

A topological space

X
X

is pseudoradial if each of its non closed subsets

A
A

has a sequence (not necessarily with countable length) convergent to outside of

A
A

. We prove the following results concerning pseudoradial spaces and the spaces

ω
∪
{
p
}

\omega \cup \{p\}

, where

p
p

is an ultrafilter on

ω
\omega

: (i) CH implies that, for every ultrafilter

p
p

on

ω
\omega

,

ω
∪
{
p
}

\omega \cup \{p\}

is a subspace of some regular pseudoradial space. (ii) There is a model in which, for each P-point

p
p

,

ω
∪
{
p
}

\omega \cup \{p\}

cannot be embedded in a regular pseudoradial space while there is a point

q
q

such that

ω
∪
{
q
}

\omega \cup \{q\}

is a subspace of a zero-dimensional Hausdorff pseudoradial space.
On the proof of characterizations of the exponential dichotomy
Authors: Minh Nguyen
Published: July 2002

We describe explicitly the generator of the evolutionary semigroup associated with the evolutionary operator generated by the linear differential equation

x
′

(
t
)
=
A
(
t
)
x
(
t
)

x’(t)=A(t)x(t)

. From this we give a short proof of some known characterizations of the exponential dichotomy of the above mentioned equation.
Projections from L(E,F) onto K(E,F)
Authors: Saphar Pierre
Published: July 2002

LetEEandFFbe two infinite dimensional real Banach spaces. The following question is classical and long-standing. Are the following properties equivalent? a) There exists a projection from the spaceL(E,F)L(E,F)of continuous linear operators onto the spaceK(E,F)K(E,F)of compact linear operators. b)L(E,F)=K(E,F)L(E,F)=K(E,F). The answer is positive in certain cases, in particular ifEEorFFhas an unconditional basis. It seems that there are few results in the direction of a general solution. For example, suppose thatEEandFFare reflexive and thatEEorFFhas the approximation property. Then, ifL(E,F)≠K(E,F)L(E,F)\ne K(E,F), there is no projection of norm 1, fromL(E,F)L(E,F)ontoK(E,F)K(E,F). In this paper, one obtains, in particular, the following result:Theorem.LetFFbe a real Banach space which is reflexive (resp. with a separable dual), of infinite dimension, and such thatF∗F^*has the approximation property. Letλ\lambdabe a real scalar with1>λ>21>\lambda >2. ThenFFcan be equivalently renormed such that, for any projectionPPfromL(F)L(F)ontoK(F)K(F), one has‖P‖≥λ\|P\|\ge \lambda. One gives also various results with two spacesEEandFF.
Norm of convolution by operator-valued functions on free groups
Authors: Buchholz Artur
Published: July 2002

We present a connection between the Leinert sets and the non-crossing two-partitions and we use this connection to give a simple proof of the free Khintchine inequality in discrete non-commutative

L
p

L_p

-spaces. Moreover we extend the inequality of Haagerup-Pisier,
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-vertical-bar sigma-summation Underscript g element-of upper S Endscripts lamda left-parenthesis g right-parenthesis circled-times a Subscript g Baseline double-vertical-bar Subscript upper C Sub Subscript lamda Sub Superscript asterisk Subscript left-parenthesis upper F Sub Subscript n Subscript right-parenthesis circled-times upper A Baseline less-than-or-equal-to 2 max left-brace right-brace comma double-vertical-bar double-vertical-bar sigma-summation sigma-summation element-of element-of gS times times ag asterisk ag 12 comma double-vertical-bar double-vertical-bar sigma-summation sigma-summation element-of element-of gS times times agag asterisk 12 comma">

‖

∑

g
∈
S

λ
(
g
)
⊗

a
g

‖

C
λ
∗

(

F
n

)
⊗
A

≤
2
max

{

‖

∑

g
∈
S

a
g
∗

a
g

‖

1
2

,

‖

∑

g
∈
S

a
g

a
g
∗

‖

1
2

}

,

\left \| \sum _{g\in S} \lambda (g)\otimes a_g\right \|_{C_\lambda ^*(F_n)\otimes A} \le 2\max \left \{\left \| \sum _{g\in S} a_g^*a_g\right \|^{\frac 12}, \left \|\sum _{g\in S} a_g a_g^*\right \|^{\frac 12}\right \},

\]
where

λ
\lambda

is the left regular representation of the group

F
n

F_n

,

a
g

a_g

are elements of the

C
∗

C^*

-algebra

A
A

, and

S
S

is the set of the words with length one, to the set

S
S

of the words with arbitrary fixed length.
The Furuta inequality with negative powers
Authors: Tanahashi Kôtarô
Published: July 2002

Let

A
,
B
∈
B
(
H
)

A, B \in B(H)

be bounded linear operators on a Hilbert space

H
H

satisfying

O
≤
B
≤
A

O\leq B\leq A

. Furuta showed the operator inequality

(

A

r

B

p

A

r

)

1
q

≤

(A^{r}B^{p}A^{r})^{\frac {1}{q}}\leq

A

p
+
2
r

q

A^{\frac {p+2r}{q}}

as long as positive real numbers

p
,
q
,
r

p , q, r

satisfy

p
+
2
r
≤
(
1
+
2
r
)
q

p+2r\leq (1+2r)q

and

1
≤
q

1\leq q

. In this paper, we show this inequality is valid if negative real numbers

p
,
q
,
r

p, q, r

satisfy a certain condition. Also, we investigate the optimality of that condition.
On Swan conductors for Brauer groups of curves over local fields
Authors: Yamazaki Takao
Published: July 2002

For an element

w
w

of the Brauer group of a curve over a local field, we define the “Swan conductor”

sw
⁡
(
w
)

\operatorname {sw}(w)

of

w
w

, which measures the wildness of the ramification of

w
w

. We give a relation between

sw
⁡
(
w
)

\operatorname {sw}(w)

and Swan conductors for Brauer groups of henselian discrete valuation fields defined by Kato.
A simple proof of a curious congruence by Sun
Authors: Shan Zun , Wang Edward
Published: July 2002

In this note, we give a simple and elementary proof of the following curious congruence which was established by Zhi-Wei Sun:
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript k equals 1 Overscript left-parenthesis p minus 1 right-parenthesis slash 2 Endscripts StartFraction 1 Over k dot 2 Superscript k Baseline EndFraction identical-to sigma-summation Underscript k equals 1 Overscript left-bracket 3 p slash 4 right-bracket Endscripts StartFraction left-parenthesis negative 1 right-parenthesis Superscript k minus 1 Baseline Over k EndFraction left-parenthesis normal m normal o normal d p right-parenthesis period">

∑

k
=
1

(
p
−
1
)

/

2

1

k
⋅

2
k

≡

∑

k
=
1

[
3
p

/

4
]

(
−
1

)

k
−
1

k

(

m
o
d

p
)
.

\sum ^{(p-1)/2}_{k=1}\frac {1}{k\cdot 2^k}\equiv \sum ^{[3p/4]}_{k=1} \frac {(-1)^{k-1}}{k}\quad (\mathrm {mod}\,p).

\]
On the nonrationality of rigid Lie algebras
Authors: Bermudez J. , Goze M.
Published: July 2002

In his thesis, Carles made the following conjecture: Every rigid Lie algebra is defined on the field

Q
Q

. This was quite an interesting question because a positive answer would give a nice explanation of the fact that simple Lie algebras are defined over

Q
Q

. The goal of this note is to provide a large number of examples of rigid but nonrational and nonreal Lie algebras.
The holomorphic extension of 𝐻^{𝑝}-CR functions on tube submanifolds
Authors: Boggess Al
Published: July 2002

We consider the set of CR functions on a connected tube submanifold of

C
n

C^n

satisfying a uniform bound on the

L
p

L^p

-norm in the tube direction. We show that all such CR functions holomorphically extend to

H
p

H^p

functions on the convex hull of the tube (

1
≤
p
≤
∞

1 \leq p \leq \infty

). The

H
p

H^p

-norm of the extension is shown to be the same as the uniform

L
p

L^p

-norm in the tube direction of the CR function.
Surfaces with harmonic inverse mean curvature in space forms
Authors: Fujioka Atsushi
Published: July 2002

We define surfaces with harmonic inverse mean curvature in space forms and generalize a theorem due to Lawson by which surfaces of constant mean curvature in one space form isometrically correspond to those in another. We also obtain an immersion formula, which gives a deformation family for these surfaces.
Cut-point spaces
Authors: Honari B. , Bahrampour Y.
Published: July 2002

The notion of a cut-point space is introduced as a connected topological space without any non-cut point. It is shown that a cut-point space is infinite. The non-cut point existence theorem is proved for general (not necessarily

T
1

T_1

) topological spaces to show that a cut-point space is non-compact. Also, the class of irreducible cut-point spaces is studied and it is shown that this class (up to homeomorphism) has exactly one member: the Khalimsky line.
An extension of the work of V. Guillemin on complex powers and zeta functions of elliptic pseudodifferential operators
Authors: Bucicovschi Bogdan
Published: July 2002

The purpose of this note is to extend the methods and results of Guillemin on elliptic self-adjoint pseudodifferential operators of order one, from operators defined on smooth functions on a closed manifold to operators defined on smooth sections in a vector bundle. The case of bundles of Hilbert modules of finite type over a finite von Neumann algebra will also be treated.
Polynomially convex hulls of graphs on the sphere
Authors: Jimbo Toshiya , Sakai Akira
Published: July 2002

Let

Σ
\Sigma

be the graph of a continuous map of the unit sphere of

C

n

\mathbb C^n

into

C

m

\mathbb C^m

, and

h
(
Σ
)

h(\Sigma )

the polynomially convex hull of

Σ
\Sigma

. Several examples of

h
(
Σ
)

h(\Sigma )

for

n
=
m
>
1

n=m>1

are given, which have different properties from the known ones for

n
>
m

n>m

.