March 2016 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Karim Khanaki
by Bentuo Zheng (bzheng) 29 Mar '16

29 Mar '16

This is an announcement for the paper “Tsirelson’s space has NIP” by Karim Khanaki. Abstract: E. Odell showed that Tsirelson's space is strongly separable. This result implies that Tsirelson's space has the non independence property (NIP). The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.08134

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

29 Mar '16

This is an announcement for the paper “A Bourgain-like property of Banach spaces with no copies of $c_0$” by A. Perez and M Raja. Abstract: We give a characterization of the existence of copies of $c_0$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pelczynski theorem about weakly unconditionally Cauchy series. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1603.08706

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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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