This is an announcement for the paper "Corrigendum to Approximation
by C^{p}-smooth, Lipschitz functions on Banach spaces"
[J. Math. Anal. Appl., 315 (2006), 599-605]" by R. Fry.
Abstract: In this erratum, we recover the results from an earlier paper
of the author's which contained a gap. Specifically, we prove that if X
is a Banach space with an unconditional basis and admits a C^{p}-smooth,
Lipschitz bump function, and Y is a convex subset of X, then any uniformly
continuous function f: Y->R can be uniformly approximated by Lipschitz,
C^{p}-smooth functions K:X->R. Also, if Z is any Banach space and f:X->Z
is L-Lipschitz, then the approximates K:X->Z can be chosen CL-Lipschitz
and C^{p}-smooth, for some constant C depending only on X.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Citation: Journal of Mathematical Analysis and Applications, Volume 348,
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0810.3881
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This is an announcement for the paper "Bidual as a weak nonstandard hull"
by Siu-Ah Ng.
Abstract: We construct the weak nonstandard hull of a normed linear space
X from *X (the nonstandard extension of X) using the weak topology on
X. The bidual (i.e. the second dual) X'' is shown to be isometrically
isomorphic to the weak nonstandard hull of X. Examples and applications
to C*-algebras are given, including a simple proof of the Sherman-Takeda
Theorem. As a consequence, the weak nonstandard hull of a C*-algebra is
always a von Neumann algebra. Moreover a natural representation of the
Arens product is given.
Archive classification: math.FA math.LO math.OA
Mathematics Subject Classification: 46L05, 03H05, 26E3,5 46S20
Remarks: 14 pages
The source file(s), bidual.tex: 38768 bytes, is(are) stored in gzipped
form as 0810.3090.gz with size 11kb. The corresponding postcript file
has gzipped size 87kb.
Submitted from: ngs(a)ukzn.ac.za
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http://front.math.ucdavis.edu/0810.3090
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http://arXiv.org/abs/0810.3090
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This is an announcement for the paper "$L^1$ is complemented in $L^{\infty
*}$" by Javier Guachalla H.
Abstract: We show $L^1$ is complemented in the dual space $L^{\infty *}$
Archive classification: math.FA
The source file(s), l1cmplm.TEX: 2401 bytes, is(are) stored in gzipped
form as 0810.2354.gz with size 1kb. The corresponding postcript file
has gzipped size 29kb.
Submitted from: jguachallah(a)gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0810.2354
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http://arXiv.org/abs/0810.2354
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This is an announcement for the paper "On extensions of d.c. functions
and convex functions" by Libor Vesely and Ludek Zajicek.
Abstract: We show how our recent results on compositions of d.c. functions
(and mappings) imply positive results on extensions of d.c. functions
(and mappings). Examples answering two natural relevant questions are
presented. Two further theorems, concerning extendability of continuous
convex functions from a closed subspace of a normed linear space,
complement recent results of J.Borwein, V.Montesinos and J.Vanderwerff.
Archive classification: math.FA math.GM
Mathematics Subject Classification: 52A41; 26B25; 46B99
Remarks: 16 pages
The source file(s), RozsirDCfinal.tex: 48466 bytes, is(are) stored in
gzipped form as 0810.1433.gz with size 15kb. The corresponding postcript
file has gzipped size 110kb.
Submitted from: Libor.Vesely(a)mat.unimi.it
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http://front.math.ucdavis.edu/0810.1433
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http://arXiv.org/abs/0810.1433
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This is an announcement for the paper "Convexity of Chebyshev sets in
Hilbert spaces" by Hadi Haghshenas.
Abstract: The aim of this paper is state of conditions that ensure the
convexity of a Chebyshev sets in Hilbert spaces .
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 4 Pages
The source file(s), CONVEXITYOFCEBYSEVSETSINHILBERTSPACES.tex: 8784
bytes, is(are) stored in gzipped form as 0810.0772.gz with size 3kb. The
corresponding postcript file has gzipped size 36kb.
Submitted from: h_haghshenas60(a)yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0810.0772
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This is an announcement for the paper "A review on some geometric results
of the Smulian's theorem on Frechet differentiability of norms" by
A. Assadi,HADI Haghshenas and H. Hosseini Guive.
Abstract: In this paper, we prove the Smulian s theorem on Frechet
differentiability of norm,and present some of its geometric results
concerning the Gateaux and Frechet differentiability of norm and
properties of the allied space and its dual such as reflexivity and
strict convexity.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 4 Pages
The source file(s),
AREVIEWONSOMEGEOMETRICRESULTSOFTHESMULIANSTHEOREMONFRECHETDIFFERENTIABILITYOFNORMS.tex:
10646 bytes, is(are) stored in gzipped form as 0810.0773.gz with size
4kb. The corresponding postcript file has gzipped size 42kb.
Submitted from: h_haghshenas60(a)yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0810.0773
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This is an announcement for the paper "Convexity of Chebyshev sets through
differentiability of distance function" by Assadi, Hadi Haghshenas,
and Hosseini Guive.
Abstract: The aim of this paper is to present some equivalent conditions
that ensure the convexity of a Chebyshev set. To do so, we use Gateaux
differentiability of the distance function
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 4 pages
The source file(s),
CONVEXITYOFCEBYSEVSETSTHROUGHDIFFERENTIABILITYOFDISTANCEFUNCTION.tex:
10884 bytes, is(are) stored in gzipped form as 0810.0587.gz with size
4kb. The corresponding postcript file has gzipped size 41kb.
Submitted from: h_haghshenas60(a)yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0810.0587
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http://arXiv.org/abs/0810.0587
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This is an announcement for the paper "Differentiability of Banach spaces
via constructible sets" by Hadi Haghshenas.
Abstract: the main goal of this paper is to prove that any Banach space X
, that every dual ball in X** is weak* separable, or every weak* closed
convex subset in X**is weak* separable , or every norm-closed convex set
in X* is constructible, admits an equivalent Frechet differentiable norm.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
Remarks: 5 pages
The source file(s),
DIFFERENTIABILITYOFBANACHSPACESVIACONSTRUCTIBLESETS.tex: 12164 bytes,
is(are) stored in gzipped form as 0810.0586.gz with size 5kb. The
corresponding postcript file has gzipped size 43kb.
Submitted from: h_haghshenas60(a)yahoo.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/0810.0586
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This is an announcement for the paper "On Banach spaces containing $l_p$
or $c_0$" by George Androulakis, Nigel Kalton, and Adi Tcaciuc.
Abstract: We use the Gowers block Ramsey theorem to characterize Banach
spaces containing isomorphs of $\ell_p$ (for some $1 \leq p < \infty$)
or $c_0$.
Archive classification: math.FA
Mathematics Subject Classification: 46B20; 46B40; 46B03
The source file(s), ellpAndKalTca.tex: 22204 bytes, is(are) stored in
gzipped form as 0810.0325.gz with size 7kb. The corresponding postcript
file has gzipped size 72kb.
Submitted from: giorgis(a)math.sc.edu
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http://front.math.ucdavis.edu/0810.0325
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