Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Peter G. Casazza and Janet C. Tremain
by Dale Alspach 10 Jan '07

10 Jan '07

This is an announcement for the paper "the paving conjecture is equivalent to the paving conjecture for triangular matrices" by Peter G. Casazza and Janet C. Tremain. Abstract: We resolve a 25 year old problem by showing that The Paving Conjecture is equivalent to The Paving Conjecture for Triangular Matrices. Archive classification: Functional Analysis Mathematics Subject Classification: 47A20, 47B99, 46B07 The source file(s), 12.5.06.tex: 20512 bytes, is(are) stored in gzipped form as 0701101.gz with size 7kb. The corresponding postcript file has gzipped size 87kb. Submitted from: pete(a)math.missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0701101 or http://arXiv.org/abs/math.FA/0701101 or by email in unzipped form by transmitting an empty message with subject line uget 0701101 or in gzipped form by using subject line get 0701101 to: math(a)arXiv.org.

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Abstract of a paper by J. Talponen
by Dale Alspach 02 Jan '07

02 Jan '07

This is an announcement for the paper "On weakly extremal structures in Banach spaces" by J. Talponen. Abstract: This paper deals with the interplay of the geometry of the norm and the weak topology in Banach spaces. Both dual and intrinsic connections between weak forms of rotundity and smoothness ared discussed. Weakly exposed points, weakly locally uniformly rotund spaces, smoothness, duality and the interplay of all the above are studied. An example of a Banach space, which is midpoint locally uniformly rotund but not weakly locally uniformly rotund is given. Archive classification: Functional Analysis Mathematics Subject Classification: 46B20; 46A20 Remarks: 12 pages The source file(s), wg.tex: 45886 bytes, is(are) stored in gzipped form as 0701009.gz with size 13kb. The corresponding postcript file has gzipped size 103kb. 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/math.FA/0701009 or http://arXiv.org/abs/math.FA/0701009 or by email in unzipped form by transmitting an empty message with subject line uget 0701009 or in gzipped form by using subject line get 0701009 to: math(a)arXiv.org.

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Abstract of a paper by Bernhard Lamel
by Dale Alspach 02 Jan '07

02 Jan '07

This is an announcement for the paper "Local automorphisms of the Hilbert ball" by Bernhard Lamel. Abstract: We prove an analogue of Alexander's Theorem for holomorphic mappings of the unit ball in a complex Hilbert space: Every holomorphic mapping which takes a piece of the boundary of the unit ball into the boundary of the unit ball and whose differential at some point of this boundary is onto is the restriction of an automorphism of the ball. We also show that it is enough to assume that the mapping is only Gateaux-holomorphic. Archive classification: Complex Variables; Functional Analysis Mathematics Subject Classification: 32H12, 46G20, 46T25, 58C10 The source file(s), L_hilbertball/definitions.tex: 3255 bytes, L_hilbertball/hilbertball2.bbl: 1011 bytes, L_hilbertball/hilbertball2.tex: 24133 bytes, is(are) stored in gzipped form as 0612688.tar.gz with size 10kb. The corresponding postcript file has gzipped size 89kb. Submitted from: bernhard.lamel(a)univie.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.CV/0612688 or http://arXiv.org/abs/math.CV/0612688 or by email in unzipped form by transmitting an empty message with subject line uget 0612688 or in gzipped form by using subject line get 0612688 to: math(a)arXiv.org.

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Abstract of a paper by Thomas Jech
by Dale Alspach 23 Dec '06

23 Dec '06

This is an announcement for the paper "Algebraic characterizations of measure algebras" by Thomas Jech. Abstract: We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra. Archive classification: Functional Analysis; Logic Mathematics Subject Classification: 28 The source file(s), Measure.tex: 31579 bytes, is(are) stored in gzipped form as 0612598.gz with size 9kb. The corresponding postcript file has gzipped size 89kb. Submitted from: jech(a)math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0612598 or http://arXiv.org/abs/math.FA/0612598 or by email in unzipped form by transmitting an empty message with subject line uget 0612598 or in gzipped form by using subject line get 0612598 to: math(a)arXiv.org.

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Abstract of a paper by R Haydon, A Molto and J Orihuela
by Dale Alspach 13 Dec '06

13 Dec '06

This is an announcement for the paper "Spaces of functions with countably many discontinuities" by R Haydon, A Molto and J Orihuela. Abstract: Let $\Gamma$ be a Polish space and let $K$ be a separable and poointwise compact set of real-valued functions on $\Gamma$. It is shown that if each function in $K$ has only countably many discontinuities then $C(K)$ may be equipped with a $T_p$-lower semicontinuous and locally uniformly convex norm, equivalent to the supremum norm. Archive classification: Functional Analysis; General Topology Mathematics Subject Classification: 46B03; 54H05 The source file(s), fewdiscfinal.tex: 56379 bytes, is(are) stored in gzipped form as 0612307.gz with size 18kb. The corresponding postcript file has gzipped size 144kb. Submitted from: richard.haydon(a)bnc.ox.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0612307 or http://arXiv.org/abs/math.FA/0612307 or by email in unzipped form by transmitting an empty message with subject line uget 0612307 or in gzipped form by using subject line get 0612307 to: math(a)arXiv.org.

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Abstract of a paper by Joel A. Tropp
by Dale Alspach 06 Dec '06

06 Dec '06

This is an announcement for the paper "A new proof of the paving property for uniformly bounded matrices" by Joel A. Tropp. Abstract: This note presents a new proof of an important result due to Bourgain and Tzafriri that provides a partial solution to the Kadison--Singer problem. The result shows that every unit-norm matrix whose entries are relatively small in comparison with its dimension can be paved by a partition of constant size. That is, the coordinates can be partitioned into a constant number of blocks so that the restriction of the matrix to each block of coordinates has norm less than one half. The original proof of Bourgain and Tzafriri involves a long, delicate calculation. The new proof relies on the systematic use of symmetrization and Khintchine inequalities to estimate the norm of some random matrices. The key new ideas are due to Rudelson. Archive classification: Metric Geometry; Functional Analysis; Probability Mathematics Subject Classification: 46B07; 47A11; 15A52 Remarks: 12 pages The source file(s), bdd-ks-v1.bbl: 2693 bytes, bdd-ks-v1.tex: 41646 bytes, macro-file.tex: 8551 bytes, is(are) stored in gzipped form as 0612070.tar.gz with size 15kb. The corresponding postcript file has gzipped size 99kb. Submitted from: jtropp(a)umich.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0612070 or http://arXiv.org/abs/math.MG/0612070 or by email in unzipped form by transmitting an empty message with subject line uget 0612070 or in gzipped form by using subject line get 0612070 to: math(a)arXiv.org.

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Abstract of a paper by Jeff Cheeger and Bruce Kleiner
by Dale Alspach 02 Dec '06

02 Dec '06

This is an announcement for the paper "Differentiating maps into L^1 and the geometry of BV functions" by Jeff Cheeger and Bruce Kleiner. Abstract: This is one of a series of papers examining the interplay between differentiation theory for Lipschitz maps, X--->V, and bi-Lipschitz nonembeddability, where X is a metric measure space and V is a Banach space. Here, we consider the case V=L^1 where differentiability fails. We establish another kind of differentiability for certain X, including R^n and H, the Heisenberg group with its Carnot-Cartheodory metric. It follows that H does not bi-Lipschitz embed into L^1, as conjectured by J. Lee and A. Naor. When combined with their work, this provides a natural counter example to the Goemans-Linial conjecture in theoretical computer science; the first such counterexample was found by Khot-Vishnoi. A key ingredient in the proof of our main theorem is a new connection between Lipschitz maps to L^1 and functions of bounded variation, which permits us to exploit recent work on the structure of BV functions on the Heisenberg group. Archive classification: Metric Geometry; Differential Geometry; Functional Analysis; Group The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.MG/0611954 or http://arXiv.org/abs/math.MG/0611954 or by email in unzipped form by transmitting an empty message with subject line uget 0611954 or in gzipped form by using subject line get 0611954 to: math(a)arXiv.org.

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Abstract of a paper by Morten Nielsen
by Dale Alspach 30 Nov '06

30 Nov '06

This is an announcement for the paper "Trigonometric quasi-greedy bases for $L^p(\bT;w)$" by Morten Nielsen. Abstract: We give a complete characterization of $2\pi$-periodic weights $w$ for which the usual trigonometric system forms a quasi-greedy basis for $L^p(\bT;w)$, i.e., bases for which simple thresholding approximants converge in norm. The characterization implies that this can happen only for $p=2$ and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis. Archive classification: Functional Analysis Mathematics Subject Classification: 42C15 Remarks: 8 pages The source file(s), trig_quasi_greedy.tex: 23971 bytes, is(are) stored in gzipped form as 0611892.gz with size 8kb. The corresponding postcript file has gzipped size 98kb. Submitted from: mnielsen(a)math.wustl.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0611892 or http://arXiv.org/abs/math.FA/0611892 or by email in unzipped form by transmitting an empty message with subject line uget 0611892 or in gzipped form by using subject line get 0611892 to: math(a)arXiv.org.

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Abstract of a paper by Morten Nielsen
by Dale Alspach 30 Nov '06

30 Nov '06

This is an announcement for the paper "An example of an almost greedy uniformly bounded orthonormal basis for $L_p([0,1])$" by Morten Nielsen. Abstract: We construct a uniformly bounded orthonormal almost greedy basis for $L_p([0,1])$, $1<p<\infty$. The example shows that it is not possible to extend Orlicz's theorem, stating that there are no uniformly bounded orthonormal unconditional bases for $L_p([0,1])$, $p\not=2$, to the class of almost greedy bases. Archive classification: Functional Analysis Mathematics Subject Classification: 42C20 Remarks: 8 pages The source file(s), QG.tex: 23612 bytes, is(are) stored in gzipped form as 0611890.gz with size 8kb. The corresponding postcript file has gzipped size 96kb. Submitted from: mnielsen(a)math.wustl.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0611890 or http://arXiv.org/abs/math.FA/0611890 or by email in unzipped form by transmitting an empty message with subject line uget 0611890 or in gzipped form by using subject line get 0611890 to: math(a)arXiv.org.

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Abstract of a paper by Bernhard Haak and Jan van Neerven
by Dale Alspach 30 Nov '06

30 Nov '06

This is an announcement for the paper "Uniformly gamma-radonifying families of operators and the linear stochastic Cauchy problem in Banach spaces" by Bernhard Haak and Jan van Neerven. Abstract: We introduce the notion of uniform $\gamma$--radonification of a family of operators, which unifies the notions of $R$--boundedness of a family of operators and $\gamma$--radonification of an individual operator. We study the the properties of uniformly $\gamma$--radonifying families of operators in detail and apply our results to the stochastic abstract Cauchy problem $$ dU(t) = AU(t)\,dt + B\,dW(t), \quad U(0)=0. $$ Here, $A$ is the generator of a strongly continuous semigroup of operators on a Banach space $E$, $B$ is a bounded linear operator from a separable Hilbert space $H$ into $E$, and $W_H$ is an $H$--cylindrical Brownian motion. Archive classification: Functional Analysis Mathematics Subject Classification: 47B10; 35R15; 46B09; 46B50; 47D06; 60B11; 60H15 Remarks: submitted for publication The source file(s), unif-gamma.arxiv.tex: 75863 bytes, is(are) stored in gzipped form as 0611724.gz with size 23kb. The corresponding postcript file has gzipped size 152kb. Submitted from: bernhard.haak(a)math.uni-karlsruhe.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0611724 or http://arXiv.org/abs/math.FA/0611724 or by email in unzipped form by transmitting an empty message with subject line uget 0611724 or in gzipped form by using subject line get 0611724 to: math(a)arXiv.org.

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