This is an announcement for the paper "Maurey's factorization theory
for operator spaces" by Marius Junge and Javier Parcet.
Abstract: We provide an operator space version of Maurey's factorization
theorem. The main tool is an embedding result of independent
interest. Applications for operator spaces and noncommutative Lp spaces
are included.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 46L07; 47B10
Remarks: 26 pages
The source file(s), Maurey.tex: 91710 bytes, is(are) stored in gzipped
form as 0901.1928.gz with size 28kb. The corresponding postcript file
has gzipped size 160kb.
Submitted from: javier.parcet(a)uam.es
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This is an announcement for the paper "A general Pettis integral and
applications to transition semigroups" by Markus Kunze.
Abstract: Motivated by applications to transition semigroups, we introduce
the notion of a norming dual pair and study a Pettis-type integral
on such pairs. In particular, we establish a sufficient condition for
integrability. We also introduce and study a class of semigroups on such
dual pairs which are an abstract version of transition semigroups. Using
our results, we prove conditions ensuring that a semigroup consisting of
kernel operators is Laplace transformable such that the Laplace transform
consists of kernel operators again.
Archive classification: math.FA
Mathematics Subject Classification: 46G10, 47D03, 60J35
Remarks: 19 pages, no figures
The source file(s), pettists.tex: 64277 bytes, is(are) stored in gzipped
form as 0901.1771.gz with size 19kb. The corresponding postcript file
has gzipped size 122kb.
Submitted from: m.c.kunze(a)tudelft.nl
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http://front.math.ucdavis.edu/0901.1771
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http://arXiv.org/abs/0901.1771
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This is an announcement for the paper "Isometries on extremely non-complex
Banach spaces" by Piotr Koszmider, Miguel Martin and Javier Meri .
Abstract: We construct an example of a real Banach space whose group of
surjective isometries reduces to $\pm\Id$, but the group of surjective
isometries of its dual contains the group of isometries of a separable
infinite-dimensional Hilbert space as a subgroup. To do so, we present
examples of extremely non-complex Banach spaces (i.e.\ spaces $X$ such
that $\|\Id + T^2\|=1+\|T^2\|$ for every bounded linear operator $T$
on $X$) which are not of the form $C(K)$, and we study the surjective
isometries on this class of Banach spaces.
Archive classification: math.FA math.OA
Mathematics Subject Classification: Primary: 46B04. Secondary: 46B10,
46B20, 46E15, 47A99
Remarks: 20 pages
The source file(s), KoszmiderMartinMeri.tex: 84147 bytes, is(are)
stored in gzipped form as 0901.1512.gz with size 24kb. The corresponding
postcript file has gzipped size 138kb.
Submitted from: mmartins(a)ugr.es
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http://front.math.ucdavis.edu/0901.1512
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This is an announcement for the paper "Tensor extension properties of
C(K)-representations and applications to unconditionality" by Christoph
Kriegler and Christian Le Merdy.
Abstract: Let K be any compact set. The C^*-algebra C(K) is nuclear
and any bounded homomorphism from C(K) into B(H), the algebra of all
bounded operators on some Hilbert space H, is automatically completely
bounded. We prove extensions of these results to the Banach space setting,
using the key concept of R-boundedness. Then we apply these results to
operators with a uniformly bounded H^\infty-calculus, as well as to
unconditionality on L^p. We show that any unconditional basis on L^p
`is' an unconditional basis on L^2 after an appropriate change of density.
Archive classification: math.OA math.FA
Mathematics Subject Classification: 47A60; 46B28
The source file(s), CK-Art.tex: 73146 bytes, is(are) stored in gzipped
form as 0901.1025.gz with size 22kb. The corresponding postcript file
has gzipped size 145kb.
Submitted from: clemerdy(a)univ-fcomte.fr
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0901.1025
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This is an announcement for the paper "Almost invariant half-spaces
of operators on Banach spaces" by George Androulakis, Alexey I. Popov,
Adi Tcaciuc and Vladimir G. Troitsky.
Abstract: We introduce and study the following modified version of the
Invariant Subspace Problem: whether every operator T on a Banach space
has an almost invariant half-space, that is, a subspace Y of infinite
dimension and infinite codimension such that Y is of finite codimension
in T(Y). We solve this problem in the affirmative for a large class of
operators which includes quasinilpotent weighted shift operators on l_p
(1 \le p < \infty) or c_0.
Archive classification: math.FA
Mathematics Subject Classification: 47A15
Remarks: 13 pages
The source file(s), invariantV9.tex: 38986 bytes, is(are) stored in
gzipped form as 0901.0752.gz with size 12kb. The corresponding postcript
file has gzipped size 95kb.
Submitted from: vtroitsky(a)math.ualberta.ca
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http://arXiv.org/abs/0901.0752
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This is an announcement for the paper "Weak$^*$ dentability index
of spaces $C([0,\alpha])$" by Petr Hajek, Gilles Lancien and Antonin
Prochazka.
Abstract: We compute the weak$^*$-dentability index
of the spaces $C(K)$ where $K$ is a countable compact
space. Namely $\mbox{Dz}(C([0,\omega^{\omega^\alpha}])) =
\omega^{1+\alpha+1}$, whenever $0\le\alpha<\omega_1$. More generally,
$\mbox{Dz}(C(K))=\omega^{1+\alpha+1}$ if $K$ is a scattered compact whose
height $\eta(K)$ satisfies $\omega^\alpha<\eta(K)\leq \omega^{\alpha+1}$
with an $\alpha$ countable.
Archive classification: math.FA
Mathematics Subject Classification: 46B20, 46B03, 46E15
The source file(s), delta4revised.tex: 28188 bytes, is(are) stored in
gzipped form as 0901.0681.gz with size 9kb. The corresponding postcript
file has gzipped size 78kb.
Submitted from: protony(a)centrum.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0901.0681
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This is an announcement for the paper "Quasiminimality in mixed Tsirelson
spaces" by Antonis Manoussakis and Anna Maria Pelczar.
Abstract: We prove that mixed Tsirelson spaces T[(M_n,\theta_n)_n], where
M_n=A_n for all n or M_n=S_n for all n, are quasiminimal. We prove that
under certain assumptions on the sequence (\theta_n)_n the dual spaces
are also quasiminimal.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46B45
Remarks: 25 pages
The source file(s), quasiminimality.tex: 87433 bytes, is(are) stored in
gzipped form as 0812.4711.gz with size 26kb. The corresponding postcript
file has gzipped size 163kb.
Submitted from: anna.pelczar(a)im.uj.edu.pl
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This is an announcement for the paper "A note on fragmentability and
weak-G_delta sets" by V. P. Fonf, R. J. Smith and S. Troyanski.
Abstract: In terms of fragmentability, we describe a new class of
Banach spaces which do not contain weak-G_delta open bounded subsets. In
particular, none of these spaces is isomorphic to a separable polyhedral
space.
Archive classification: math.FA
The source file(s), frag-w-gdelta6.tex: 18701 bytes, is(are) stored in
gzipped form as 0812.4690.gz with size 7kb. The corresponding postcript
file has gzipped size 70kb.
Submitted from: smith(a)math.cas.cz
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http://front.math.ucdavis.edu/0812.4690
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