Banach

banach@mathdept.okstate.edu

2549 discussions

Abstract of a paper by Rainis Haller, Katrlin Pirk and Mart Poldvere
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Diametral strong diameter two property of Banach spaces is stable under direct sums with $1$-norm” by Rainis Haller, Katrlin Pirk and Mart Poldvere. Abstract: We prove that the diametral strong diameter $2$ property of a Banach space (meaning that, in convex combinations of relatively weakly open subsets of its unit ball, every point has an "almost diametral" point) is stable under $1$-sums, i.e., the direct sum of two spaces with the diametral strong diameter $2$ property equipped with the $1$-norm has again this property. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.08082

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Abstract of a paper by Hendrik Vogt and Jurgen Voigt
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Bands in $L_p$-spaces” by Hendrik Vogt and Jurgen Voigt. Abstract: For a general measure space $(\Omega, \mu)$ it is shown that for every band $M$ in $L_p(\mu)$ there exists a decomposition $\mu=\mu’+\mu’’$ such that $M=L_p(\mu’)=\{f\in L_p(\mu): f=0 \mu’’-a.e.\}$. The theory is illustrated by an example, with an application to absorption semigroups. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.07681

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Abstract of a paper by Yves Raynaud
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “On the Banach space structure of Banach lattices with disjointness preserving isometries: ultraroots and axiomatizability” by Yves Raynaud. Abstract: Let $C$ be an axiomatizable class of order continuous real or complex Banach lattices, that is, this class is closed under isometric vector lattice isomorphisms and ultraproducts, and the complementary class is closed under ultrapowers. We show that if linear isometric embeddings of members of $C$ in their ultrapowers preserve disjointness, the class $C^B$ of Banach spaces obtained by forgetting the Banach lattice structure is still axiomatizable. Moreover if $C$ coincides with its "script class" $SC$, so does $C^B$ with $SC^B$. This allows us to give new examples of axiomatizable classes of Banach spaces, namely certain Musielak-Orlicz spaces, Nakano spaces, and mixed norm spaces. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.07510

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Abstract of a paper M. Daher
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Radon-Nkikodym property in $L(X, Y)$” by M. Daher. Abstract: Let $X$ be a separable Banach space and $Y$ a space which has the Radon-Nikodym property. In this work, we show that $L(X, Y)$ has the Radon-Nikodym property, if $L(X, Y)$ is weakly locally uniformly convex or if $L(X, Y)$ is a weakly compactly generated space. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.07127

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Abstract of a paper by C. Bargetz, J. Kakol and W. Kubis
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “A separable Frechet space of almost universal disposition” by C. Bargetz, J. Kakol and W. Kubis. Abstract: The Gurarii space is the unique separable Banach space $G$ which is of almost universal disposition for finite-dimensional Banach spaces, which means that for every $\epsilon>0$, for all finite-dimensional normed spaces $E\subset F$, for every isometric embedding $e: E\rightarrow G$ there exists an $\epsilon$-isometric embedding $f: F\rightarrow G$ such that $f|E=e$. We show that $G^N$ with a special sequence of semi-norms is of almost universal disposition for finite-dimensional graded Frechet spaces. The construction relies heavily on the universal operator on the Gurarii space, recently constructed by Garbulinska-Wegrzyn and the third author. This yields in particular that $G^N$ is universal in the class of all separable Frechet spaces. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.06361

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Abstract of a paper by Aldo J. Lazar
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “A selection theorem for Banach bundles and applications” by Aldo J. Lazar. Abstract: It is shown that certain lower semi-continuous maps from a paracompact space to the family of closed subsets of the bundle space of a Banach bundle admit continuous selections. This generalization of the theorem of Douady, dal Soglio-Herault, and Hofmann on the fullness of Banach bundles has applications to establishing conditions under which the induced maps between the spaces of sections of Banach bundles are onto. Another application is to a generalization of the theorem of Bartle and Graves for Banach bundle maps that are onto their images. Other applications of the selection theorem are to the study begun by Gierz of the M-ideals of the space of bounded sections. A class of Banach bundles that generalizes the class of locally trivial bundles is introduced and some properties of the Banach bundles in this class are discussed. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.06198

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Abstract of a paper by Steven J. Dilworth, Smbat Gogyan, Denka Kutzarova and Thomas Schlumprecht
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “On the boundedness of threshold operators in $L_1[0,1]$ with respect to the Haar basis” by Steven J. Dilworth, Smbat Gogyan, Denka Kutzarova and Thomas Schlumprecht. Abstract: We prove a near-unconditionality property for the normalized Haar basis of $L_1[0,1]$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.05732

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Abstract of a paper by Sergio A. Perez
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Banach spaces of linear operators and homogeneous polynomials without the approximation property” by Sergio A. Perez. Abstract: We present many examples of Banach spaces of linear operators and homogeneous polynomials without the approximation property, thus improving results of Dineen and Mujica [11] and Godefroy and Saphar [13]. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.05489

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Abstract of a paper by Eleftherios Kastis
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “The parabolic algebra on Banach spaces” by Eleftherios Kastis. Abstract: The parabolic algebra was introduced by Katavolos and Power, in 1997, as the operator algebra acting on $L_2(R)$ that is weakly generated by the translation and multiplication semigroups. In particular, they proved that this algebra is reflexive and is equal to the Fourier binest algebra, that is, to the algebra of operators that leave invariant the subspaces of the Volterra nest and its analytic counterpart. We prove that a similar result holds for the corresponding algebras acting on $L_p(R)$, where $1<p<\infty$. It is also shown that the reflexive closures of the Fourier binests on $L_p(R)$, are all order isomorphic for $1<p<\infty$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.03426

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Abstract of a paper Hauke Dirksen
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “The best constant in the Khintchine inequality of the Orlicz space $L_{\Phi_2}$ for equidistributed random variables on spheres” by Hauke Dirksen. Abstract: We compute the best constant in the Khintchine inequality for equidistributed random variables on the $N$-sphere in the Orlicz space $L_{\Phi_2}$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.02471

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