Banach February 2015

banach@mathdept.okstate.edu

2 participants
28 discussions

Abstract of a paper by Dale E. Alspach and Bunyamin Sari
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "Separable elastic Banach spaces are universal" by Dale E. Alspach and Bunyamin Sari. Abstract: A Banach space $X$ is elastic if there is a constant $K$ so that whenever a Banach space $Y$ embeds into $X$, then there is an embedding of $Y$ into $X$ with constant $K$. We prove that $C[0,1]$ embeds into separable infinite dimensional elastic Banach spaces, and therefore they are universal for all separable Banach spaces. This confirms a conjecture of Johnson and Odell. The proof uses incremental embeddings into $X$ of $C(K)$ spaces for countable compact $K$ of increasing complexity. To achieve this we develop a generalization of Bourgain's basis index that applies to unconditional sums of Banach spaces and prove a strengthening of the weak injectivity property of these $C(K)$ that is realized on special reproducible bases. Archive classification: math.FA Mathematics Subject Classification: 46B03 (primary), 46B25 (secondary) Remarks: 27 pages Submitted from: alspach(a)math.okstate.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.03791 or http://arXiv.org/abs/1502.03791

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Abstract of a paper by Yousef Estaremi
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "weighted conditional type operators between different Orlicz spaces" by Yousef Estaremi. Abstract: In this note we consider weighted conditional type operators between different Orlicz spaces and generalized conditional type Holder inequality that we defined in [2]. Then we give some necessary and sufficient conditions for boundedness of weighted conditional type operators. As a consequence we characterize boundedness of weighted conditional type operators and multiplication operators between different L^p-spaces. Finally, we give some upper and lower bounds for essential norm of weighted conditional type operators. Archive classification: math.FA Remarks: 13 pages Submitted from: estaremi(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.03422 or http://arXiv.org/abs/1502.03422

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Abstract of a paper by William B. Johnson, Tomasz Kania, and Gideon Schechtman
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "Closed ideals of operators on and complemented subspaces of Banach spaces of functions with countable support" by William B. Johnson, Tomasz Kania, and Gideon Schechtman. Abstract: Let $\lambda$ be an infinite cardinal number and let $\ell_\infty^c(\lambda)$ denote the subspace of $\ell_\infty(\lambda)$ consisting of all functions which assume at most countably many non zero values. We classify all infinite dimensional complemented subspaces of $\ell_\infty^c(\lambda)$, proving that they are isomorphic to $\ell_\infty^c(\kappa)$ for some cardinal number $\kappa$. Then we show that the Banach algebra of all bounded linear operators on $\ell_\infty^c(\lambda)$ or $\ell_\infty(\lambda)$ has the unique maximal ideal consisting of operators through which the identity operator does not factor. Using similar techniques, we obtain an alternative to Daws' approach description of the lattice of all closed ideals of $\mathscr{B}(X)$, where $X = c_0(\lambda)$ or $X=\ell_p(\lambda)$ for some $p\in [1,\infty)$, and we classify the closed ideals of $\mathscr{B}(\ell_\infty^c(\lambda))$ that contain the ideal of weakly compact operators. Archive classification: math.FA Submitted from: tomasz.marcin.kania(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.03026 or http://arXiv.org/abs/1502.03026

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Abstract of a paper by Daria Ghilli and Paolo Salani
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "Quantitative Borell-Brascamp-Lieb inequalities for compactly power concave functions (and some applications)" by Daria Ghilli and Paolo Salani. Abstract: We strengthen, in two different ways, the so called Borell-Brascamp- Lieb inequality in the class of power concave functions with compact support. As examples of applications we obtain two quantitative versions of the Brunn- Minkowski inequality and of the Urysohn inequality for torsional rigidity. Archive classification: math.AP math.FA Submitted from: ghilli(a)math.unipd.it The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.02810 or http://arXiv.org/abs/1502.02810

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Abstract of a paper by Anna Kaminska and Damian Kubiak
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "The Daugavet property in the Musielak-Orlicz spaces" by Anna Kaminska and Damian Kubiak. Abstract: We show that among all Musielak-Orlicz function spaces on a $\sigma$-finite non-atomic complete measure space equipped with either the Luxemburg norm or the Orlicz norm the only spaces with the Daugavet property are $L_1$, $L_{\infty}$, $L_1\oplus_1 L_{\infty}$ and $L_1\oplus_{\infty} L_{\infty}$. We obtain in particular complete characterizations of the Daugavet property in the weighted interpolation spaces, the variable exponent Lebesgue spaces (Nakano spaces) and the Orlicz spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46E30, 47B38 Remarks: 20 pages. To appear in Journal of Mathematical Analysis and The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.02760 or http://arXiv.org/abs/1502.02760

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Abstract of a paper by Aude Dalet, Pedro L. Kaufmann, and Antonin Prochazka
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "Free spaces over ultrametric spaces are never isometric to $\ell_1$" by Aude Dalet, Pedro L. Kaufmann, and Antonin Prochazka. Abstract: We show that the Lipschitz free space over an ultrametric space is not isometric to $\ell_1(\Gamma)$ for any set $\Gamma$. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B20 Submitted from: antonin.prochazka(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.02719 or http://arXiv.org/abs/1502.02719

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Abstract of a paper by Eftychios Glakousakis and Sophocles Mercourakis
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "Examples of infinite dimensional Banach spaces without infinite equilateral sets" by Eftychios Glakousakis and Sophocles Mercourakis. Abstract: An example of an infinite dimensional and separable Banach space is given, that is not isomorphic to a subspace of l1 with no infinite equilateral sets. Archive classification: math.FA Mathematics Subject Classification: Primary 46B20, Secondary 46B04 Remarks: 22 pages Submitted from: smercour(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.02500 or http://arXiv.org/abs/1502.02500

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Abstract of a paper by Hossein Dehghan
by alspach＠math.okstate.edu 16 Feb '15

16 Feb '15

This is an announcement for the paper "Characterizing of Inner Product Spaces by the Mapping $n_{x,y}$" by Hossein Dehghan. Abstract: For the vectors $x$ and $y$ in a normed linear spaces $X$, the mapping $n_{x,y}: \mathbb{R}\to \mathbb{R}$ is defined by $n_{x,y}(t)=\|x+ty\|$. In this note, comparing the mappings $n_{x,y}$ and $n_{y,x}$ we obtain a simple and useful characterization of inner product spaces. Archive classification: math.FA math.CA Submitted from: hossein.dehgan(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.02250 or http://arXiv.org/abs/1502.02250

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Abstract of a paper by Daniel Pellegrino, Pilar Rueda and Enrique Sanchez-Perez
by alspach＠math.okstate.edu 09 Feb '15

09 Feb '15

This is an announcement for the paper "Improving integrability via absolute summability: a general version of Diestel's Theorem" by Daniel Pellegrino, Pilar Rueda and Enrique Sanchez-Perez. Abstract: A classical result by J. Diestel establishes that the composition of a summing operator with a (strongly measurable) Pettis integrable function gives a Bochner integrable function. In this paper we show that a much more general result is possible regarding the improvement of the integrability of vector valued functions by the summability of the operator. After proving a general result, we center our attention in the particular case given by the $(p,\sigma)$-absolutely continuous operators, that allows to prove a lot of special results on integration improvement for selected cases of classical Banach spaces ---including $C(K)$, $L^p$ and Hilbert spaces--- and operators ---$p$-summing, $(q,p)$-summing and $p$-approximable operators---. Archive classification: math.FA Submitted from: pellegrino(a)pq.cnpq.br The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.01970 or http://arXiv.org/abs/1502.01970

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Abstract of a paper by Antonio Aviles and Witold Marciszewski
by alspach＠math.okstate.edu 09 Feb '15

09 Feb '15

This is an announcement for the paper "Extension operators on balls and on spaces of finite sets" by Antonio Aviles and Witold Marciszewski. Abstract: We study extension operators between spaces $\sigma_n(2^X)$ of subsets of $X$ of cardinality at most $n$. As an application, we show that if $B_H$ is the unit ball of a nonseparable Hilbert space $H$, equipped with the weak topology, then, for any $0<\lambda<\mu$, there is no extension operator $T: C(\lambda B_H)\to C(\mu B_H)$. Archive classification: math.FA math.GN Mathematics Subject Classification: 46B26, 46E15, 54C35, 54H05 Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1502.01875 or http://arXiv.org/abs/1502.01875

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Banach February 2015