- Banach - mathdept.okstate.edu

Abstract of a paper by S. Waleed Noor
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Embeddings of M\"{u}ntz spaces: composition operators" by S. Waleed Noor. Abstract: Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We discuss how properties of the embedding $M_\Lambda^2\subset L^2(\mu)$, where $\mu$ is a finite positive Borel measure on the interval $[0,1]$, have immediate consequences for composition operators on $M^2_\Lambda$. We give criteria for composition operators to be bounded, compact, or to belong to the Schatten--von Neumann ideals. Archive classification: math.FA Mathematics Subject Classification: 46E15, 46E20, 46E35 Citation: Integral Equations Operator Theory, Springer, 2012 Remarks: 15 Pages Submitted from: waleed_math(a)hotmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4719 or http://arXiv.org/abs/1207.4719

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Abstract of a paper by Manor Mendel and Assaf Naor
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Nonlinear spectral calculus and super-expanders" by Manor Mendel and Assaf Naor. Abstract: Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Ces\`aro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space. Archive classification: math.MG math.CO math.FA Remarks: Some of the results of this paper were announced in arXiv:0910.2041. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4705 or http://arXiv.org/abs/1207.4705

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Abstract of a paper by Diana Ojeda-Aristizabal
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "A norm for Tsirelson's Banach space" by Diana Ojeda-Aristizabal. Abstract: We give an expression for the norm of the space constructed by Tsirelson. The implicit equation satisfied by this norm is dual to the implicit equation for the norm of the dual of Tsirelson space given by Figiel and Johnson. The expression can be modified to give the norm of the dual of any mixed Tsirelson space. In particular, our results can be adapted to give the norm for the dual of Schlumprecht space. Archive classification: math.FA Mathematics Subject Classification: 46B20 Submitted from: dco34(a)cornell.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4504 or http://arXiv.org/abs/1207.4504

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Abstract of a paper by Peer Christian Kunstmann and Alexander Ullmann
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Rs-sectorial operators and generalized Triebel-Lizorkin spaces" by Peer Christian Kunstmann and Alexander Ullmann. Abstract: We introduce a notion of generalized Triebel-Lizorkin spaces associated with sectorial operators in Banach function spaces. Our approach is based on holomorphic functional calculus techniques. Using the concept of $\mathcal{R}_s$-sectorial operators, which in turn is based on the notion of $\mathcal{R}_s$-bounded sets of operators introduced by Lutz Weis, we obtain a neat theory including equivalence of various norms and a precise description of real and complex interpolation spaces. Another main result of this article is that an $\mathcal{R}_s$-sectorial operator always has a bounded $H^\infty$-functional calculus in its associated generalized Triebel-Lizorkin spaces. Archive classification: math.FA Mathematics Subject Classification: 46E30, 47A60, 47B38 (Primary), 42B25 (Secondary) Remarks: 44 pages Submitted from: alexander.ullmann(a)gmx.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.4217 or http://arXiv.org/abs/1207.4217

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Abstract of a paper by Michal Kraus
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Coarse and uniform embeddings between Orlicz sequence spaces" by Michal Kraus. Abstract: We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper Matuszewska-Orlicz indices. Archive classification: math.FA Mathematics Subject Classification: 46B80, 46B20 Remarks: 12 pages Submitted from: mkraus(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3967 or http://arXiv.org/abs/1207.3967

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Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Large structures made of nowhere $L^p$ functions" by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini. Abstract: We say that a real-valued function $f$ defined on a positive Borel measure space $(X,\mu)$ is nowhere $q$-integrable if, for each nonvoid open subset $U$ of $X$, the restriction $f|_U$ is not in $L^q(U)$. When $X$ is a Polish space and $\mu$ satisfies some natural properties, we show that certain sets of functions which are $p$-integrable for some $p$'s but nowhere $q$-integrable for some other $q$'s ($0<p,q<\infty$) admit large linear and algebraic structures within them. In our Polish space context, the presented results answer a question from Bernal-Gonz\'alez [L. Bernal-Gonz\'alez, Algebraic genericity and strict-order integrability, Studia Math. 199(3)(2010), 279--293], and improves and complements results of several authors. Archive classification: math.FA Submitted from: leoime(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3818 or http://arXiv.org/abs/1207.3818

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Abstract of a paper by Christian Rosendal
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Rigidity of commuting affine actions on reflexive Banach spaces" by Christian Rosendal. Abstract: We give a simple argument to show that if {\alpha} is an afﬁne isometric action of a product G x H of topological groups on a reﬂexive Banach space X with linear part {\pi}, then either {\pi}(H) ﬁxes a unit vector or {\alpha}|G almost ﬁxes a point on X. It follows that any afﬁne isometric action of an abelian group on a reﬂexive Banach space X, whose linear part ﬁxes no unit vectors, almost ﬁxes points on X. Archive classification: math.GR math.FA Submitted from: rosendal.math(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3731 or http://arXiv.org/abs/1207.3731

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Abstract of a paper by Mikolaj Krupski and Witold Marciszewski
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "Some remarks on universality properties of $\ell_\infty / c_0$" by Mikolaj Krupski and Witold Marciszewski. Abstract: We prove that if continuum is not a Kunen cardinal, then there is a uniform Eberlein compact space $K$ such that the Banach space $C(K)$ does not embed isometrically into $\ell_\infty/c_0$. We prove a similar result for isomorphic embeddings. We also construct a consistent example of a uniform Eberlein compactum whose space of continuous functions embeds isomorphically into $\ell_\infty/c_0$, but fails to embed isometrically. As far as we know it is the first example of this kind. Archive classification: math.FA Mathematics Subject Classification: Primary 46B26, 46E15, Secondary 03E75 Submitted from: krupski(a)impan.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3722 or http://arXiv.org/abs/1207.3722

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Abstract of a paper by Anil Kumar Karn and Deba Prasad Sinha
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "An operator summability of sequences in Banach spaces" by Anil Kumar Karn and Deba Prasad Sinha. Abstract: Let $1 \leq p <\infty$. A sequence $\lef x_n \rig$ in a Banach space $X$ is defined to be $p$-operator summable if for each $\lef f_n \rig \in l^{w^*}_p(X^*)$, we have $\lef \lef f_n(x_k)\rig _k \rig _n \in l^s_p(l_p)$. Every norm $p$-summable sequence in a Banach space is operator $p$-summable, while in its turn every operator $p$-summable sequence is weakly $p$-summable. An operator $T \in B(X, Y)$ is said to be $p$-limited if for every $\lef x_n \rig \in l_p^w(X)$, $\lef Tx_n \rig$ is operator $p$-summable. The set of all $p$-limited operators form a normed operator ideal. It is shown that every weakly $p$-summable sequence in $X$ is operator $p$-summable if and only if every operator $T \in B(X, l_p)$ is $p$-absolutely summing. On the other hand every operator $p$-summable sequence in $X$ is norm $p$-summable if and only if every $p$-limited operator in $B(l_{p'}, X)$ is absolutely $p$-summing. Moreover, this is the case if and only if $X$ is a subspace of $L_p(\mu )$ for some Borel measure $\mu$. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B28, 46B50 Remarks: 16 pages Submitted from: anilkarn(a)niser.ac.in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3620 or http://arXiv.org/abs/1207.3620

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Abstract of a paper by Tomasz Kochanek
by alspach＠math.okstate.edu 26 Jul '12

26 Jul '12

This is an announcement for the paper "$\mathcal F$-bases with individual brackets in Banach spaces" by Tomasz Kochanek. Abstract: We provide a partial answer to the question of Vladimir Kadets whether given an $\mathcal F$-basis of a~Banach space $X$, with respect to some filter $\mathcal F\subset \mathcal P(\mathbb N)$, the coordinate functionals are continuous. The answer is positive if the character of $\mathcal F$ is less than $\mathfrak{p}$. In this case every $\mathcal F$-basis with individual brackets is an $M$-basis with brackets determined by a set from $\mathcal F$. Archive classification: math.FA Submitted from: t.kania(a)lancaster.ac.uk The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1207.3097 or http://arXiv.org/abs/1207.3097

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