This is an announcement for the paper "On strict inclusions in
hierarchies of convex bodies" by V.Yaskin.
Abstract: Let $\mathcal I_k$ be the class of convex $k$-intersection
bodies in $\mathbb{R}^n$ (in the sense of Koldobsky) and $\mathcal
I_k^m$ be the class of convex origin-symmetric bodies all of whose
$m$-dimensional central sections are $k$-intersection bodies. We
show that 1) $\mathcal I_k^m\not\subset \mathcal I_k^{m+1}$, $k+3\le
m<n$, and 2) $\mathcal I_l \not\subset \mathcal I_k$, $1\le k<l <
n-3$.
Archive classification: math.FA
Mathematics Subject Classification: 52A20, 52A21, 46B04
Remarks: 10 pages
The source file(s), Yaskin.tex: 31833 bytes, is(are) stored in
gzipped form as 0707.1471.gz with size 10kb. The corresponding
postcript file has gzipped size 82kb.
Submitted from: vyaskin(a)math.ou.edu
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/0707.1471
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http://arXiv.org/abs/0707.1471
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This is an announcement for the paper "Equimeasurabily and isometries
in noncommutative Lp-spaces" by Mikael de la Salle.
Abstract: We prove some noncommutative analogues of a theorem by
Rudin and Plotkin about equimeasurability and isometries in L_p-spaces.
Let 0<p<\infty, p not an even integer. The main result of this paper
states that in the category of unital subspaces of noncommutative
probability Lp-spaces, the unital completely isometric maps come
from *-isomorphisms of the underlying von Neumann algebras.
Unfortunately we are only able to treat the case of bounded operators.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 46L53; 46L51; 47L05
Remarks: 11 pages
The source file(s), article_arxiv.bbl: 2056 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0707.0427
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http://arXiv.org/abs/0707.0427
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This is an announcement for the paper "A Maurey type result for
operator spaces" by Marius Junge and Hun Hee Lee.
Abstract: The little Grothendieck theorem for Banach spaces says
that every bounded linear operator between $C(K)$ and $\ell_2$ is
2-summing. However, it is shown in \cite{J05} that the operator
space analogue fails. Not every cb-map $v : \K \to OH$ is completely
2-summing. In this paper, we show an operator space analogue of
Maurey's theorem : Every cb-map $v : \K \to OH$ is $(q,cb)$-summing
for any $q>2$ and hence admits a factorization $\|v(x)\| \leq c(q)
\|v\|_{cb} \|axb\|_q$ with $a,b$ in the unit ball of the Schatten
class $S_{2q}$.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47L25; 46B07
Remarks: 29 pages
The source file(s), MaureyTypeResultOS.tex: 99707 bytes, is(are)
stored in gzipped form as 0707.0152.gz with size 25kb. The corresponding
postcript file has gzipped size 184kb.
Submitted from: lee.hunhee(a)gmail.com
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0707.0152
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http://arXiv.org/abs/0707.0152
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This is an announcement for the paper "Tsirelson like operator
spaces" by Hun Hee Lee.
Abstract: We construct nontrivial examples of weak-$C_p$ ($1\leq p
\leq \infty$) operator spaces with the local operator space structure
very close to $C_p = [R, C]_{\frac{1}{p}}$. These examples are
non-homogeneous Hilbertian operator spaces, and their constructions
are similar to that of 2-convexified Tsirelson's space by W. B.
Johnson.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 47L25; 46B07
Remarks: 19 pages
The source file(s), TsirelsonLikeOS.tex: 54208 bytes, is(are) stored
in gzipped form as 0707.0147.gz with size 13kb. The corresponding
postcript file has gzipped size 113kb.
Submitted from: lee.hunhee(a)gmail.com
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0707.0147
or
http://arXiv.org/abs/0707.0147
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This is an announcement for the paper "Markov type of Alexandrov
spaces of nonnegative curvature" by Shin-ichi Ohta.
Abstract: We prove that Alexandrov spaces $X$ of nonnegative curvature
have Markov type 2 in the sense of Ball. As a corollary, any Lipschitz
continuous map from a subset of $X$ into a 2-uniformly convex Banach
space is extended as a Lipschitz continuous map on the entire space
$X$.
Archive classification: math.MG math.FA
Mathematics Subject Classification: 46B20, 53C21, 60J10
Remarks: 16 pages
The source file(s), type+.tex: 40468 bytes, is(are) stored in gzipped
form as 0707.0102.gz with size 11kb. The corresponding postcript
file has gzipped size 103kb.
Submitted from: sohta(a)math.kyoto-u.ac.jp
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0707.0102
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http://arXiv.org/abs/0707.0102
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uget 0707.0102
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