This is an announcement for the paper "Upper bound for isometric
embeddings \ell_2^m\to\ell_p^n" by Yuri I. Lyubich.
Abstract: The isometric embeddings $\ell_{2;K}^m\to\ell_{p;K}^n$
($m\geq 2$, $p\in 2\N$) over a field $K\in{R, C, H}$ are considered,
and an upper bound for the minimal $n$ is proved. In the commutative
case ($K\neq H$) the bound was obtained by Delbaen, Jarchow and
Pe{\l}czy{\'n}ski (1998) in a different way.
Archive classification: math.FA
Mathematics Subject Classification: 46B04
Remarks: 5 pages
The source file(s), upbound.bbl: 1810 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0712.0214
or
http://arXiv.org/abs/0712.0214
or by email in unzipped form by transmitting an empty message with
subject line
uget 0712.0214
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to: math(a)arXiv.org.
This is an announcement for the paper "Coorbit spaces for dual
pairs" by J. G. Christensen and G. Olafsson.
Abstract: This paper contains a generalization of the coorbit space
theory initiated in the 1980's by H.G. Feichtinger and K.H. Groechenig.
This theory has been a powerful tool in characterizing Banach spaces
of functions with the use of integrable representations of locally
compact groups. Examples are a wavelet characterization of the Besov
spaces and a characterization of some Bergman spaces by the discrete
series representation of $\mathrm{SL}_2(\mathbb{R})$. We suggest a
generalization of the coorbit space theory, which is able to account
for a wider range of Banach spaces and also for quasi Banach spaces.
A few examples of Banach spaces which could not be covered by the
previous theory are described.
Archive classification: math.FA math.RT
Mathematics Subject Classification: 43A15,42B35 (Primary) 22D12
(Secondary)
The source file(s), coorbit.bbl: 4205 bytes
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0711.4120
or
http://arXiv.org/abs/0711.4120
or by email in unzipped form by transmitting an empty message with
subject line
uget 0711.4120
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This is an announcement for the paper "Small subspaces of L_p" by
R.Haydon, E.Odell, Th.Schlumprecht.
Abstract: We prove that if $X$ is a subspace of $L_p$ $(2<p<\infty)$
then either $X$ embeds isomorphically into $\ell_p \oplus \ell_2$
or $X$ contains a subspace $Y$, which is isomorphic to $\ell_p(\ell_2)$.
We also give an intrinsic characterization of when $X$ embeds into
$\ell_p \oplus \ell_2$ in terms of weakly null trees in $X$ or
equivalently in terms of the ``infinite asymptotic game'' played
in $X$. This solves problems concerning small subspaces of $L_p$
originating in the 1970's. The techniques used were developed over
several decades, the most recent being that of weakly null trees
developed in the 2000's.
Archive classification: math.FA
Mathematics Subject Classification: 46E30
The source file(s), smallsubspaces.tex: 99982 bytes, is(are) stored
in gzipped form as 0711.3919.gz with size 31kb. The corresponding
postcript file has gzipped size 185kb.
Submitted from: schlump(a)math.tamu.edu
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0711.3919
or
http://arXiv.org/abs/0711.3919
or by email in unzipped form by transmitting an empty message with
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uget 0711.3919
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This is an announcement for the paper "Convex-transitivity and
function spaces" by Jarno Talponen.
Abstract: It is shown that the Bochner space L^{p}([0,1],X) is
convex-transitive for any convex-transitive X and 1\leq p\leq \infty.
If H is an infinite-dimensional Hilbert space and C_{0}(L) is
convex-transitive, then C_{0}(L,H) is convex-transitive. Some new
fairly concrete examples of convex-transitive spaces are provided.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46E40
The source file(s), Rotations3.tex: 62608 bytes, is(are) stored in
gzipped form as 0711.3768.gz with size 19kb. The corresponding
postcript file has gzipped size 119kb.
Submitted from: talponen(a)cc.helsinki.fi
The paper may be downloaded from the archive by web browser from
URL
http://front.math.ucdavis.edu/0711.3768
or
http://arXiv.org/abs/0711.3768
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Dear Colleagues,
We would like to invite you to participate in the summer school on
"Fourier analytic and probabilistic methods in geometric functional
analysis and convexity" in August 13-20, 2008.
The school is being organized by the NSF funded Focused Research Group
collaborative project on the same subject
(http://www.math.ucdavis.edu/~geofunction/). It is oriented towards
graduate students, postdocs and researchers who wish to get an
introduction to the subject. The school will feature several series's
of lectures. Confirmed speakers include
Alexander Barvinok (University of Michigan),
Piotr Indyk (Massachusetts Institute of Technology),
Fedor Nazarov (University of Wisconsin-Madison),
Krzysztof Oleszkiewicz (University of Warsaw),
Rolf Schneider (University of Freiburg),
Santosh S. Vempala (Georgia Institute of Technology).
The school will be hosted by the Department of Mathematical Sciences at
Kent State University in August 13-20, 2008. Kent is located in the
suburbs of Cleveland, Ohio, where summers are quite beautiful. We plan
to spend one of the evenings at the nearby Blossom Music Center, the
summer home of the renowned Cleveland Orchestra.
With NSF funding we will be able to cover local, and, probably, travel
expenses for a limited number of participants, so we ask you to reply as
soon as possible to Dmitry Ryabogin (ryabogin(a)math.kent.edu) or Artem
Zvavitch (zvavitch(a)math.kent.edu). Graduate students and Postdoctoral
fellows are especially encouraged to apply.
For further information and breaking news, please, consult
http://www.math.kent.edu/math/FAPR.cfm
Again, please note that your early response will help us gauge the needs
for housing, lecture room(s), etc. We hope to be sending out information
regarding housing by the end of December.
We hope to see you in Kent next August.
Best Regards,
The organizing committee
Alex Koldobsky
Mark Rudelson
Dmitry Ryabogin
Stanislaw Szarek
Roman Vershynin
Elisabeth Werner
Artem Zvavitch
I neglected to shut off the automated password reminder on the old server.
The message with hardy.math.okstate.edu at the bottom is the correct one.
Sorry for any confusion this may have caused.
Dale Alspach