This is an announcement for the paper "Operators on asymptotic $\ell_p$
spaces which are not compact perturbations of a multiple of the
identity" by Kevin Beanland.
Abstract: We give sufficient conditions on an asymptotic $\ell_p$
(for $1 < p < \infty$) Banach space which ensure the space admits
an operator which is not a compact perturbation of a multiple of the
identity. These conditions imply the existence of strictly singular
non-compact operators on the HI spaces constructed by G. Androulakis
and the author and by I. Deliyanni and A. Manoussakis. Additionally we
show that under these same conditions on the space $X$, $\ell_\infty$
embeds isomorphically into the space of bounded linear operators on $X$.
Archive classification: math.FA
The source file(s), SSnonCPT.tex: 51728 bytes, is(are) stored in gzipped
form as 0908.1107.gz with size 16kb. The corresponding postcript file
has gzipped size 120kb.
Submitted from: kbeanland(a)gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0908.1107
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http://arXiv.org/abs/0908.1107
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This is an announcement for the paper "On Y. Nievergelt's inversion
formula for the Radon transform" by Elena Ournycheva and Boris Rubin.
Abstract: We generalize Y. Nievergelt's inversion method for the Radon
transform on lines in the 2-plane to the $k$-plane Radon transform of
continuous and $L^p$ functions on $R^n$ for all $1\leq k<n$.
Archive classification: math.FA
Mathematics Subject Classification: Primary 42C40; Secondary 44A12
Remarks: 9 pages
The source file(s), niev-amsproc4.tex: 29069 bytes, is(are) stored in
gzipped form as 0908.0492.gz with size 10kb. The corresponding postcript
file has gzipped size 78kb.
Submitted from: elo10(a)pitt.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0908.0492
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http://arXiv.org/abs/0908.0492
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This is an announcement for the paper "Banach SSD spaces and classes of
monotone sets" by Stephen Simons.
Abstract: In this paper, we unify the theory of SSD spaces and the theory
of strongly representable sets, and we apply our results to the theory
of the various classes of maximally monotone sets. We obtain some new
results about these, as well as some new proofs of old ones.
Archive classification: math.FA
Mathematics Subject Classification: 47H05, 47N10, 46N10
The source file(s), SSDMONarxiv.tex: 116002 bytes, is(are) stored in
gzipped form as 0908.0383.gz with size 29kb. The corresponding postcript
file has gzipped size 133kb.
Submitted from: simons(a)math.ucsb.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0908.0383
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http://arXiv.org/abs/0908.0383
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This is an announcement for the paper "Sharp quantitative isoperimetric
inequalities in the $L^1$ Minkowski plane" by Benoit Kloeckner.
Abstract: We prove that a plane domain which is almost isoperimetric
(with respect to the $L^1$ metric) is close to a square whose sides
are parallel to the coordinates axis. Closeness is measured either by
$L^\infty$ Haussdorf distance or Fraenkel asymmetry. In the first case,
we determine the extremal domains.
Archive classification: math.FA math.DG
Mathematics Subject Classification: MSC 51M16, 51M25, 49Q20
Remarks: 9 pages
The source file(s), central_square.pstex: 6034 bytes
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0907.4945
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http://arXiv.org/abs/0907.4945
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This is an announcement for the paper "Complex symmetric partial
isometries" by Stephan Ramon Garcia and Warren R. Wogen.
Abstract: An operator $T \in B(\h)$ is complex symmetric if there
exists a conjugate-linear, isometric involution $C:\h\to\h$ so that $T
= CT^*C$. We provide a concrete description of all complex symmetric
partial isometries. In particular, we prove that any partial isometry
on a Hilbert space of dimension $\leq 4$ is complex symmetric.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47B99
Citation: J. Funct. Analysis 257 (2009), 1251-1260
Remarks: 9 pages
The source file(s), CSPI.tex: 33368 bytes, is(are) stored in gzipped
form as 0907.4486.gz with size 10kb. The corresponding postcript file
has gzipped size 68kb.
Submitted from: Stephan.Garcia(a)pomona.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0907.4486
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http://arXiv.org/abs/0907.4486
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This is an announcement for the paper "On the hereditary proximity to
$\ell_1$" by Spiros A. Argyros, A. Manoussakis, and Anna M. Pelczar.
Abstract: In the first part of the paper we present and discuss concepts
of local and asymptotic hereditary proximity to \ell_1. The second part
is devoted to a complete separation of the hereditary local proximity
to \ell_1 from the asymptotic one. More precisely for every countable
ordinal \xi we construct a separable reflexive space \mathfrak{X}_\xi such
that every infinite dimensional subspace of it has Bourgain \ell_1-index
greater than \omega^\xi and the space itself has no \ell_1-spreading
model. We also present a reflexive HI space admitting no \ell_p as a
spreading model.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46B15; 03E10; 05A17
Remarks: 40 pages, submitted for publication
The source file(s), proximity.tex: 158273 bytes, is(are) stored in gzipped
form as 0907.4317.gz with size 43kb. The corresponding postcript file
has gzipped size 238kb.
Submitted from: anna.pelczar(a)im.uj.edu.pl
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0907.4317
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This is an announcement for the paper "The geometry of Euclidean
convolution inequalities and entropy" by Dario Cordero-Erausquin and
Michel Ledoux.
Abstract: The goal of this note is to show that some convolution
type inequalities from Harmonic Analysis and Information Theory,
such as Young's convolution inequality (with sharp constant), Nelson's
hypercontractivity of the Hermite semi-group or Shannon's inequality,
can be reduced to a simple geometric study of frames of $\R^2$. We shall
derive directly entropic inequalities, which were recently proved to be
dual to the Brascamp-Lieb convolution type inequalities.
Archive classification: math.FA math.PR
The source file(s), geoconv5.tex: 49291 bytes, is(are) stored in gzipped
form as 0907.2861.gz with size 16kb. The corresponding postcript file
has gzipped size 113kb.
Submitted from: cordero(a)math.jussieu.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0907.2861
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http://arXiv.org/abs/0907.2861
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