This is an announcement for the paper "Forme equivalente \`a la
condition $\Delta_2 $ et certains r\'esultats de s\'eparations
dans les espaces modulaires" by A.Hajji.
Abstract: In this paper, we present an equivalent form of the
$\Delta_2 $-condition which allow us to redefine the topological
vector space structure of a modular spaces using the \\ filter base.
We show also the characterization of closed subsets (in the sens
of this topology ) of a modular spaces which permit us to establish
some separation results in modular spaces
Archive classification: Functional Analysis
Remarks: 11p,pas de figure
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Submitted from: lphe(a)fsr.ac.ma
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This is an announcement for the paper "On norm closed ideals in
L(\ell_p\oplus\ell_q)" by B. Sari, Th. Schlumprecht, N. Tomczak-Jaegermann,
and V.G. Troitsky.
Abstract: It is well known that the only proper non-trivial norm-closed
ideal in the algebra L(X) for X=\ell_p (1 \le p < \infty) or X=c_0
is the ideal of compact operators. The next natural question is to
describe all closed ideals of L(\ell_p\oplus\ell_q) for 1 \le p,q
< \infty, p \neq q, or, equivalently, the closed ideals in
L(\ell_p,\ell_q) for p < q. This paper shows that for 1 < p < 2 <
q < \infty there are at least four distinct proper closed ideals
in L(\ell_p,\ell_q), including one that has not been studied before.
The proofs use various methods from Banach space theory.
Archive classification: Functional Analysis; Operator Algebras
Mathematics Subject Classification: 47L20; 47B10; 47B37
Remarks: 24 pages
Submitted from: vtroitsky(a)math.ualberta.ca
The paper may be downloaded from the archive by web browser from
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http://front.math.ucdavis.edu/math.FA/0509414
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This is an announcement for the paper "Numerical index and duality"
by Konstantin Boyko, Vladimir Kadets, Miguel Martin, and Dirk Werner.
Abstract: We present an example of a Banach space whose numerical
index is strictly greater than the numerical index of its dual,
giving a negative answer to a question which has been latent since
the beginning of the seventies. We also show a particular case in
which the numerical index of the space and the one of its dual
coincide.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20; 47A12; 46B22; 46E15
The source file(s), miguelvovakostya.tex: 34653 bytes, is(are)
stored in gzipped form as 0509374.gz with size 12kb. The corresponding
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Submitted from: werner(a)math.fu-berlin.de
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This is an announcement for the paper "The Daugavet property for
spaces of Lipschitz functions" by Yevgen Ivakhno, Vladimir Kadets
and Dirk Werner.
Abstract: For a compact metric space $K$ the space $\Lip(K)$ has
the Daugavet property if and only if the norm of every $f \in
\Lip(K)$ is attained locally. If $K$ is a subset of an $L_p$-space,
$1<p<\infty$, this is equivalent to the convexity of~$K$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B04; 46B25; 54E45
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gzipped form as 0509373.gz with size 15kb. The corresponding postcript
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Submitted from: werner(a)math.fu-berlin.de
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This is an announcement for the paper "Separated sequences in
uniformly convex Banach spaces" by Jan van Neerven.
Abstract: We prove that the unit sphere of every infinite-dimensional
uniformly convex Banach space with modulus of convexity $\delta$
contains a $(1+\frac12\delta(\frac23))$-separated sequence.
Archive classification: Functional Analysis
Mathematics Subject Classification: 46B20
Citation: Colloq. Math. 102 (2005), 147-153
Remarks: 5 pages
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Submitted from: J.vanNeerven(a)math.tudelft.nl
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http://front.math.ucdavis.edu/math.FA/0509344
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This is an announcement for the paper "Remarks on $B(H)\otimes
B(H)$" by Gilles Pisier.
Abstract: We review the existing proofs that the min and max norms
are different on $B(H)\otimes B(H)$ and give a shortcut avoiding
the consideration of non-separable families of operator spaces.
Archive classification: Operator Algebras; Functional Analysis
Mathematics Subject Classification: 46L05, 46M05, 47D15
The source file(s), remarks.BB.tex: 17702 bytes, is(are) stored in
gzipped form as 0509297.gz with size 7kb. The corresponding postcript
file has gzipped size 43kb.
Submitted from: gip(a)ccr.jussieu.fr
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This is an announcement for the paper "Conditioned square functions
for non-commutative martingales" by Narcisse Randrianantoanina.
Abstract: We prove a weak-type (1,1) inequality involving conditioned
square functions of martingales in non-commutative $L^p$-spaces
associated with finite von Neumann algebras. As application, we
determine the optimal orders for the best constants in the
non-commutative Burkholder/Rosenthal inequalities from Ann. Proba.
31 (2003), 948-995. We also discuss BMO-norms of sums of non-commuting
order independent operators.
Archive classification: Functional Analysis; Probability
Mathematics Subject Classification: 46L53; 60G42
Remarks: 38 pages
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in gzipped form as 0509226.gz with size 31kb. The corresponding
postcript file has gzipped size 136kb.
Submitted from: randrin(a)muohio.edu
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This is an announcement for the paper "Compression of uniform
embeddings into Hilbert space" by N. Brodskiy and D. Sonkin.
Abstract: If one tries to embed a metric space uniformly in Hilbert
space, how close to quasi-isometric could the embedding be? We
answer this question for finite dimensional CAT(0) cube complexes
and for hyperbolic groups. In particular, we show that the Hilbert
space compression of any hyperbolic group is 1.
Archive classification: Group Theory; Functional Analysis; Geometric
Topology
Mathematics Subject Classification: 20F69; 20F65; 46C05
Remarks: 10 pages
The source file(s), Uniform_Embeddings.tex: 27243 bytes, is(are)
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Submitted from: brodskiy(a)math.utk.edu
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http://front.math.ucdavis.edu/math.GR/0509108
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This is an announcement for the paper "Lattice structures and
spreading models" by S. J. Dilworth, E. Odell and B. Sari.
Abstract: We consider problems concerning the partial order structure
of the set of spreading models of Banach spaces. We construct
examples of spaces showing that the possible structure of these
sets include certain classes of finite semi-lattices and countable
lattices, and all finite lattices.
Archive classification: Functional Analysis
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has gzipped size 88kb.
Submitted from: bunyamin(a)unt.edu
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