This is an announcement for the paper "Two-dimensional Banach spaces
with polynomial numerical index zero" by Domingo Garcia, Bogdan Grecu,
Manuel Maestre, Miguel Martin, and Javier Meri .
Abstract: We study two-dimensional Banach spaces with polynomial numerical
indices equal to zero.
Archive classification: math.FA
Mathematics Subject Classification: Primary 46B04; Secondary 46B20,
46G25, 47A12
Remarks: 12 pages, to appear in Linear Algebra Appl
The source file(s), GarciaGrecuMaestreMartinMeri.tex: 43362 bytes, is(are)
stored in gzipped form as 0902.3234.gz with size 14kb. The corresponding
postcript file has gzipped size 103kb.
Submitted from: mmartins(a)ugr.es
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This is an announcement for the paper "Haar type and Carleson constants"
by Stefan Geiss and Paul F. X. Mueller.
Abstract: We determine the sub-collections of the dyadic intervals
that are able to detect the Haar type of a Banach space. The underlying
dichotomy is expressed in terms of the Carleson packing condition.
Archive classification: math.FA
Mathematics Subject Classification: 46B07 ; 46B20
Citation: Bull. Lond. Math. Soc. 40 (2008) 432-438
The source file(s), paper_revised050108.tex: 20601 bytes, is(are) stored
in gzipped form as 0902.1955.gz with size 7kb. The corresponding postcript
file has gzipped size 74kb.
Submitted from: pfxm(a)bayou.uni-linz.ac.at
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http://front.math.ucdavis.edu/0902.1955
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This is an announcement for the paper "Extrapolation of vector valued
rearrangement operators" by Stefan Geiss and Paul F. X. Mueller.
Abstract: We study the extrapolation properties of vector valued
rearrangement operators acting on the normalized Haar basis in $L^p_X .$
Archive classification: math.FA
Mathematics Subject Classification: 46B42, 46B70, 47B37
The source file(s), geiss_mueller.tex: 60833 bytes, is(are) stored in
gzipped form as 0902.1962.gz with size 18kb. The corresponding postcript
file has gzipped size 130kb.
Submitted from: pfxm(a)bayou.uni-linz.ac.at
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This is an announcement for the paper "Strictly singular uniform
$\lambda-$adjustment in Banach spaces" by Boris Burshteyn.
Abstract: Based on the recently introduced uniform $\lambda-$adjustment
for closed subspaces of Banach spaces we extend the concept of the
strictly singular and finitely strictly singular operators to the
sequences of closed subspaces and operators in Banach spaces and prove
theorems about lower semi--Fredholm stability. We also state some new open
questions related to strict singularity and the geometry of Banach spaces.
Archive classification: math.FA
Mathematics Subject Classification: 32A70; 46A32; 46B50; 47A53; 47A55;
47B07
Remarks: 23 pages
The source file(s), boris997paper2.tex: 117155 bytes, is(are) stored in
gzipped form as 0902.3045.gz with size 24kb. The corresponding postcript
file has gzipped size .
Submitted from: boris997(a)astound.net
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This is an announcement for the paper "Angles and polar coordinates in
real normed spaces" by Volker Thuerey.
Abstract: We try to create a wise definition of 'angle spaces'. Based on
an idea of Ivan Singer, we introduce a new concept of an angle in real
Banach spaces, which generalizes the euclidean angle in Hilbert spaces.
With this angle it is shown that in every two-dimensional subspace of a
real Banach space we can describe elements uniquely by polar coordinates.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A10
Remarks: 21 pages, 8 figures
The source file(s), anglepaper.tex: 114700 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0902.2731
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This is an announcement for the paper "Thin sets of integers in Harmonic
analysis and p-stable random Fourier series" by Pascal Lefevre, Daniel
Li, Herve Queffelec, and Luis Rodriguez-Piazza.
Abstract: We investigate the behavior of some thin sets of integers
defined through random trigonometric polynomial when one replaces Gaussian
or Rademacher variables by p-stable ones, with 1 < p < 2. We show that in
one case this behavior is essentially the same as in the Gaussian case,
whereas in another case, this behavior is entirely different.
Archive classification: math.FA
Mathematics Subject Classification: Primary: 43A46 ; secondary: 42A55;
42A61; 60G52
The source file(s), p-stableBETISfinale.tex: 72111 bytes, is(are)
stored in gzipped form as 0902.2625.gz with size 21kb. The corresponding
postcript file has gzipped size 143kb.
Submitted from: lefevre(a)euler.univ-artois.fr
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This is an announcement for the paper "Compensated compactness, separately
convex functions and interpolatory estimates between Riesz transforms and
Haar projections" by Jihoon Lee, Paul F. X. Mueller and Stefan Mueller .
Abstract: We prove sharp interpolatory estimates between Riesz Transforms
and directional Haar projections. We obtain applications to the theory
of compensated compactness and prove a conjecture of L. Tartar on
semi-continuity of separately convex integrands.
Archive classification: math.FA
Mathematics Subject Classification: 49J45; 42C15; 35B35
The source file(s), lmm.bbl: 4934 bytes
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This is an announcement for the paper "Fixed points of groups of
biholomorphic transformations of operator balls using the midpoint
property" by M.I. Ostrovskii, V.S. Shulman, and L. Turowska.
Abstract: A new techniques for proving the existence of fixed points
of groups of isometric transformations is developed. It is used to
find simpler proofs and real-case versions of previous results of the
authors. In particular, we use the obtained fixed point theorem to show
that a bounded representation in a separable, real or complex, Hilbert
space which has an invariant indefinite quadratic form with finitely
many negative squares is orthogonalizable or unitarizable (equivalent
to an orthogonal or unitary representation), respectively.
Archive classification: math.MG math.OA
Mathematics Subject Classification: 47H10; 47B50; 22D10; 54E35
The source file(s), midpoints10.tex: 42873 bytes, is(are) stored in
gzipped form as 0902.1784.gz with size 14kb. The corresponding postcript
file has gzipped size 109kb.
Submitted from: ostrovsm(a)stjohns.edu
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This is an announcement for the paper "Hereditarily indecomposable Banach
algebras of diagonal operators" by Spiros A. Argyros, Irene Deliyanni,
and Andreas G. Tolias.
Abstract: We provide a characterization of the Banach spaces $X$
with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the
property that the dual space $X^*$ is naturally isomorphic to the
space $\mathcal{L}_{diag}(X)$ of diagonal operators with respect
to $(e_n)_{n\in\mathbb{N}}$ . We also construct a Hereditarily
Indecomposable Banach space ${\mathfrak X}_D$ with a Schauder basis
$(e_n)_{n\in\mathbb{N}}$ such that ${\mathfrak X}^*_D$ is isometric
to $\mathcal{L}_{diag}({\mathfrak X}_D)$ with these Banach algebras
being Hereditarily Indecomposable. Finally, we show that every $T\in
\mathcal{L}_{diag}({\mathfrak X}_D)$ is of the form $T=\lambda I+K$,
where $K$ is a compact operator.
Archive classification: math.FA
Mathematics Subject Classification: 46B28, 47L10, 46B20, 46B03.
Remarks: 35 pages, submitted for publication to Israel J. Math
The source file(s), HI_DIAG.tex.bak: 124849 bytes, is(are) stored in
gzipped form as 0902.1646.gz with size 33kb. The corresponding postcript
file has gzipped size 188kb.
Submitted from: sargyros(a)math.ntua.gr
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This is an announcement for the paper "Isoperimetric and concentration
inequalities - Part I: Equivalence under curvature lower bound" by
Emanuel Milman.
Abstract: It is well known that isoperimetric inequalities imply in a
very general measure-metric-space setting appropriate concentration
inequalities. The former bound the boundary measure of sets as a
function of their measure, whereas the latter bound the measure of sets
separated from sets having half the total measure, as a function of
their mutual distance. We show that under a lower bound condition on the
Bakry--\'Emery curvature tensor of a Riemannian manifold equipped with a
density, completely general concentration inequalities imply back their
isoperimetric counterparts, up to dimension \emph{independent} bounds. As
a corollary, we can recover and extend all previously known (dimension
dependent) results by generalizing an isoperimetric inequality of Bobkov,
and provide a new proof that under natural convexity assumptions,
arbitrarily weak concentration implies a dimension independent linear
isoperimetric inequality. Further applications will be described in
a subsequent work. Contrary to previous attempts in this direction,
our method is entirely geometric, continuing the approach set forth by
Gromov and adapted to the manifold-with-density setting by Morgan.
Archive classification: math.DG math.FA
Remarks: 30 pages; second part involving numerous applications will appear
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0902.1560
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