This is an announcement for the paper "A compact null set containing a
differentiability point of every Lipschitz function" by Michael Doree and
Olga Maleva.
Abstract: We prove that in a Euclidean space of dimension at least
two, there exists a compact set of Lebesgue measure zero such that any
real-valued Lipschitz function defined on the space is differentiable
at some point in the set. Such a set is constructed explicitly.
Archive classification: math.FA math.CA
Mathematics Subject Classification: 46G05; 46T20
Remarks: 31 pages
The source file(s), DoreMaleva.tex: 76535 bytes, is(are) stored in gzipped
form as 0804.4576.gz with size 22kb. The corresponding postcript file
has gzipped size 144kb.
Submitted from: o.maleva(a)warwick.ac.uk
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This is an announcement for the paper "The isometry group of L^{p}(\mu,\X)
is SOT-contractible" by Jarno Talponen.
Abstract: We will show that if (\Omega,\Sigma,\mu) is an atomless
positive measure space, X is a Banach space and 1\leq p<\infty, then
the group of isometric automorphisms on the Bochner space L^{p}(\mu,X)
is contractible in the strong operator topology. We do not require \Sigma
or X above to be separable.
Archive classification: math.FA
Mathematics Subject Classification: 46B04; 46B25; 46E40
The source file(s), contr32.tex: 27449 bytes, is(are) stored in gzipped
form as 0804.4427.gz with size 9kb. The corresponding postcript file
has gzipped size 75kb.
Submitted from: talponen(a)cc.helsinki.fi
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http://front.math.ucdavis.edu/0804.4427
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http://arXiv.org/abs/0804.4427
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This is an announcement for the paper "Functional inequalities derived
from the Brunn-Minkowski inequalities for quermassintegrals" by Andrea
Colesanti and Eugenia Saorin-Gomez.
Abstract: We use Brunn-Minkowski inequalities for quermassintegrals to
deduce a family of inequalities of Poincar\'e type on the unit sphere
and on the boundary of smooth convex bodies in the $n$-dimensional
Euclidean space.
Archive classification: math.FA math.MG
Mathematics Subject Classification: 52A20; 26D10
Remarks: 15 pages
The source file(s), cs3.tex: 37802 bytes, is(are) stored in gzipped
form as 0804.3867.gz with size 12kb. The corresponding postcript file
has gzipped size 109kb.
Submitted from: colesant(a)math.unifi.it
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.3867
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http://arXiv.org/abs/0804.3867
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This is an announcement for the paper "Conditions implying the uniqueness
of the weak$^*$-topology on certain group algebras" by Matthew Daws,
Hung Le Pham and Stuart White.
Abstract: We investigate possible preduals of the measure algebra $M(G)$
of a locally compact group and the Fourier algebra $A(G)$ of a separable
compact group. Both of these algebras are canonically dual spaces and the
canonical preduals make the multiplication separately weak$^*$-continuous
so that these algebras are dual Banach algebras. In this paper we find
additional conditions under which the preduals $C_0(G)$ of $M(G)$ and
$C^*(G)$ of $A(G)$ are uniquely determined. In both cases we consider a
natural coassociative multiplication and show that the canonical predual
gives rise to the unique weak$^*$-topology making both the multiplication
separately weak$^*$-continuous and the coassociative multiplication
weak$^*$-continuous. In particular, dual cohomological properties of
these algebras are well defined with this additional structure.
Archive classification: math.FA math.OA
Mathematics Subject Classification: 43A20, 43A77
Remarks: 21 pages
The source file(s), UniquePredualFinalDraft2.tex: 73814 bytes, is(are)
stored in gzipped form as 0804.3764.gz with size 22kb. The corresponding
postcript file has gzipped size 133kb.
Submitted from: matt.daws(a)cantab.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.3764
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This is an announcement for the paper "Functional calculus extensions
on dual spaces" by Venta Terauds.
Abstract: In this note, we show that if a Banach space X has a predual,
then every bounded linear operator on X with a continuous functional
calculus admits a bounded Borel functional calculus. A consequence of
this is that on such a Banach space, the classes of finitely spectral
and prespectral operators coincide. We also apply this result to give
some sufficient conditions for an operator with an absolutely continuous
functional calculus to admit a bounded Borel one.
Archive classification: math.FA
Mathematics Subject Classification: 47B40
Remarks: 7 pages
The source file(s), func_calc_extns_terauds.tex: 24129 bytes, is(are)
stored in gzipped form as 0804.3451.gz with size 7kb. The corresponding
postcript file has gzipped size 70kb.
Submitted from: venta.terauds(a)newcastle.edu.au
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.3451
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http://arXiv.org/abs/0804.3451
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This is an announcement for the paper "R-boundedness of smooth
operator-valued functions" by Mark Veraar and Tuomas Hytonen.
Abstract: In this paper we study $R$-boundedness of operator families
$\mathcal{T}\subset \calL(X,Y)$, where $X$ and $Y$ are Banach
spaces. Under cotype and type assumptions on $X$ and $Y$ we give
sufficient conditions for $R$-boundedness. In the first part we show
that certain integral operator are $R$-bounded. This will be used to
obtain $R$-boundedness in the case that $\mathcal{T}$ is the range of
an operator-valued function $T:\R^d\to \calL(X,Y)$ which is in a certain
Besov space $B^{d/r}_{r,1}(\R^d;\calL(X,Y))$. The results will be applied
to obtain $R$-boundedness of semigroups and evolution families, and to
obtain sufficient conditions for existence of solutions for stochastic
Cauchy problems.
Archive classification: math.FA math.PR
Mathematics Subject Classification: 47B99; 46B09; 46E35; 46E40
The source file(s), rboundedsmooth_arxiv.tex: 81153 bytes, is(are)
stored in gzipped form as 0804.3313.gz with size 24kb. The corresponding
postcript file has gzipped size 142kb.
Submitted from: mark(a)profsonline.nl
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http://front.math.ucdavis.edu/0804.3313
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This is an announcement for the paper "A unified construction yielding
precisely Hilbert and James sequences spaces" by Dusan Repovs and Pavel
V. Semenov.
Abstract: Following James' approach, we shall define the Banach space
$J(e)$ for each vector $e=(e_1,e_2,...,e_d) \in \Bbb{R}^d$ with $ e_1
\ne 0$. The construction immediately implies that $J(1)$ coincides with
the Hilbert space $i_2$ and that $J(1;-1)$ coincides with the celebrated
quasireflexive James space $J$. The results of this paper show that,
up to an isomorphism, there are only the following two possibilities:
(i) either $J(e)$ is isomorphic to $l_2$ ,if $e_1+e_2+...+e_d\ne 0$
(ii) or $J(e)$ is isomorphic to $J$. Such a dichotomy also holds for
every separable Orlicz sequence space $l_M$.
Archive classification: math.GN math.FA
Mathematics Subject Classification: 54C60; 54C65; 41A65; 54C55; 54C20
The source file(s), ArchiveVersion.tex: 21648 bytes, is(are) stored in
gzipped form as 0804.3131.gz with size 8kb. The corresponding postcript
file has gzipped size 65kb.
Submitted from: dusan.repovs(a)guest.arnes.si
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.3131
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This is an announcement for the paper "Characterization of compact
subsets of $\mathcal{A}^p$ with respect to weak topology" by Hirbod Assa.
Abstract: In this brief article we characterize the
relatively compact subsets of $\mathcal{A}^p$ for the topology
$\sigma(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact
subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the weak
topology induced by $\mathcal{A}^p$, was recently employed to create
the convex risk theory of random processes. The weak compact sets of
$\mathcal{A}^p$ are important to characterize the so-called Lebesgue
property of convex risk measures, to give a complete description of the
Makcey topology on $\mathcal{R}^q$ and for their use in the optimization
theory.
Archive classification: math.PR math.FA
Remarks: 8 pages
The source file(s), compactsetsAssa.H.tex: 19008 bytes, is(are) stored in
gzipped form as 0804.2873.gz with size 6kb. The corresponding postcript
file has gzipped size 67kb.
Submitted from: assa(a)dms.umontreal.ca
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This is an announcement for the paper "Uniform lamda-adjustment and
mu-approximation in Banach spaces" by Boris Burshteyn.
Abstract: We introduce a new concept of perturbation of closed linear
subspaces and operators in Banach spaces called uniform lambda-adjustment
which is weaker than perturbations by small gap, operator norm, q-norm,
and K2-approximation. In arbitrary Banach spaces some of the classical
Fredholm stability theorems remain true under uniform lambda-adjustment,
while other fail. However, uniformly lambda-adjusted subspaces and linear
operators retain their (semi--)Fredholm properties in a Banach space
which dual is Fr\'{e}chet-Urysohn in weak* topology. We also introduce
another concept of perturbation called uniform mu-approximation which is
weaker than perturbations by small gap, norm, and compact convergence,
yet stronger than uniform lambda-adjustment. We present Fredholm stability
theorems for uniform mu-approximation in arbitrary Banach spaces and
a theorem on stability of Riesz kernels and ranges for commuting closed
essentially Kato operators. Finally, we define the new concepts of a tuple
of subspaces and of a complex of subspaces in Banach spaces, and present
stability theorems for index and defect numbers of Fredholm tuples and
complexes under uniform lambda-adjustment and uniform mu-approximation.
Archive classification: math.FA
Mathematics Subject Classification: 32A70; 46A32; 46B50; 47A53; 47A55;
47B07;
Remarks: 90 pages
The source file(s), boris997paper1.tex: 300886 bytes (looks big), is(are)
stored in gzipped form as 0804.2832.gz with size 63kb. The corresponding
postcript file has gzipped size 446kb.
Submitted from: boris997(a)astound.net
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0804.2832
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This is an announcement for the paper "Nikol'skii-type inequalities for
rearrangement invariant spaces" by Ostrovsky E. Sirota L.
Abstract: In this paper we generalize the classical Nikol'skii
inequality on the many popular classes pairs of rearrangement invariant
(r.i.) spaces and construct some examples in order to show the exactness
of our estimations.
Archive classification: math.FA
Mathematics Subject Classification: 60G17
The source file(s), Nik14_4.tex: 40903 bytes, is(are) stored in gzipped
form as 0804.2311.gz with size 14kb. The corresponding postcript file
has gzipped size 85kb.
Submitted from: leos(a)post.sce.ac.il
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http://front.math.ucdavis.edu/0804.2311
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