October 2011 - 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 Miroslav Kacena, Ondrej F.K. Kalenda and Jiri Spurny
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "Quantitative Dunford-Pettis property" by Miroslav Kacena, Ondrej F.K. Kalenda and Jiri Spurny. Abstract: We investigate possible quantifications of the Dunford-Pettis property. We show, in particular, that the Dunford-Pettis property is automatically quantitative in a sense. Further, there are two incomparable mutually dual stronger versions of a quantitative Dunford-Pettis property. We investigate their relationship with a quantitative Schur property and prove that $L^1$ spaces and $C(K)$ spaces posses both of them. We also show that several natural measures of weak non-compactness are equal in $L^1$ spaces. Archive classification: math.FA Mathematics Subject Classification: 46B03, 46B20, 47B07, 47B10 Remarks: 47 pages Submitted from: kalenda(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1110.1243 or http://arXiv.org/abs/1110.1243

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Abstract of a paper by Wieslaw Kubis and Slawomir Solecki
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "A proof of uniqueness of the Gurarii space" by Wieslaw Kubis and Slawomir Solecki. Abstract: We present a short and elementary proof of isometric uniqueness of the Gurarii space. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B20 Remarks: 6 pages Submitted from: kubis(a)math.cas.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1110.0903 or http://arXiv.org/abs/1110.0903

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Abstract of a paper by Geraldo Botelho, Daniel Cariello, Vinicius Favaro and Daniel Pellegrino
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "Maximal spaceability in topological vector spaces" by Geraldo Botelho, Daniel Cariello, Vinicius Favaro and Daniel Pellegrino. Abstract: In this paper we introduce a new technique to prove the existence of closed subspaces of maximal dimension inside sets of topological vector sequence spaces. The results we prove cover some sequence spaces not studied before in the context of spaceability and settle some questions on classical sequence spaces that remained open. Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.6863 or http://arXiv.org/abs/1109.6863

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Abstract of a paper by Jipu Ma
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "A geometry characteristic for Banach space with $c^1$-norm" by Jipu Ma. Abstract: Let $E$ be a Banach space with the $c^1$-norm $\|\cdot\|$ in $ E \backslash \{0\}$ and $S(E)=\{e\in E: \|e\|=1\}.$ In this paper, a geometry characteristic for $E$ is presented by using a geometrical construct of $S(E).$ That is, the following theorem holds : the norm of $E$ is of $c^1$ in $ E \backslash \{0\}$ if and only if $S(E)$ is a $c^1$-submanifold of $E,$ with ${\rm codim}S(E)=1.$ The theorem is very clear, however, its proof is non-trivial, which shows an intrinsic connection between the continuous differentiability of the norm $\|\cdot\|$ in $ E \backslash \{0\}$ and differential structure of $S(E).$ Archive classification: math.FA Mathematics Subject Classification: 54Exx, 46Txx, 58B20 Submitted from: huangql(a)yzu.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.6823 or http://arXiv.org/abs/1109.6823

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Abstract of a paper by Anna Pelczar-Barwacz
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "Strictly singular operators in asymptotic $\ell_p$ Banach spaces" by Anna Pelczar-Barwacz. Abstract: We present condition on higher order asymptotic behaviour of basic sequences in a Banach space ensuring the existence of bounded non-compact strictly singular operator on a subspace. We apply it in asymptotic $\ell_p$ spaces, $1\leq p<\infty$, in particular in convexified mixed Tsirelson spaces and related asymptotic $\ell_p$ HI spaces. Archive classification: math.FA Mathematics Subject Classification: 46B20, 46B06 Remarks: 19 pages Submitted from: anna.pelczar(a)im.uj.edu.pl The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5874 or http://arXiv.org/abs/1109.5874

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Abstract of a paper by Ondrej Kurka
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "Genericity of Fr\'echet smooth spaces" by Ondrej Kurka. Abstract: If a separable Banach space contains an isometric copy of every separable reflexive Fr\'echet smooth Banach space, then it contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fr\'echet smooth dual space. This improves a result of G. Godefroy and N. J. Kalton. Archive classification: math.FA Mathematics Subject Classification: Primary 46B04, 46B20, Secondary 46B15, 54H05 Remarks: 34 pages Submitted from: kurka.ondrej(a)seznam.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5726 or http://arXiv.org/abs/1109.5726

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Abstract of a paper by Anna Kaminska and Damian Kubiak
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "On the dual of Ces\`aro function space" by Anna Kaminska and Damian Kubiak. Abstract: The goal of this paper is to present an isometric representation of the dual space to Ces\`aro function space $C_{p,w}$, $1<p<\infty$, induced by arbitrary positive weight function $w$ on interval $(0,l)$ where $0<l\leqslant\infty$. For this purpose given a strictly decreasing nonnegative function $\Psi$ on $(0,l)$, the notion of essential $\Psi$-concave majorant $\hat f$ of a measurable function $f$ is introduced and investigated. As applications it is shown that every slice of the unit ball of the Ces\`aro function space has diameter 2. Consequently Ces\`aro function spaces do not have the Radon-Nikodym property, are not locally uniformly convex and they are not dual spaces. Archive classification: math.FA Mathematics Subject Classification: 46E30, 46B20, 46B42, 46B22 Remarks: 15 pages Submitted from: dmkubiak(a)memphis.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5400 or http://arXiv.org/abs/1109.5400

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Abstract of a paper by Qingying Bu, Gerard Buskes, Alexey I. Popov, Adi Tcaciuc, and Vladimir G. Troitsky
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "The 2-concavification of a Banach lattice equals the diagonal of the Fremlin tensor square" by Qingying Bu, Gerard Buskes, Alexey I. Popov, Adi Tcaciuc, and Vladimir G. Troitsky. Abstract: We investigate the relationship between the diagonal of the Fremlin projective tensor product of a Banach lattice $E$ with itself and the 2-concavification of~$E$. Archive classification: math.FA Mathematics Subject Classification: 46B42, 46M05, 46B40, 46B45 Remarks: 18 pages Submitted from: troitsky(a)ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5380 or http://arXiv.org/abs/1109.5380

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Abstract of a paper by Casey Kelleher, Daniel Miller, Trenton Osborn, and Anthony Weston
by alspach＠math.okstate.edu 07 Oct '11

07 Oct '11

This is an announcement for the paper "Strongly non embeddable metric spaces" by Casey Kelleher, Daniel Miller, Trenton Osborn, and Anthony Weston. Abstract: Enflo constructed a countable metric space that may not be uniformly embedded into any metric space of positive generalized roundness. Dranishnikov, Gong, Lafforgue and Yu modified Enflo's example to construct a locally finite metric space that may not be coarsely embedded into any Hilbert space. In this paper we meld these two examples into one simpler construction. The outcome is a locally finite metric space $(\mathfrak{Z}, \zeta)$ which is strongly non embeddable in the sense that it may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Moreover, we show that both types of embedding may be obstructed by a common recursive principle. It follows from our construction that any metric space which is Lipschitz universal for all locally finite metric spaces may not be embedded uniformly or coarsely into any metric space of non zero generalized roundness. Our construction is then adapted to show that the group $\mathbb{Z}_\omega=\bigoplus_{\aleph_0}\mathbb{Z}$ admits a Cayley graph which may not be coarsely embedded into any metric space of non zero generalized roundness. Finally, for each $p \geq 0$ and each locally finite metric space $(Z,d)$, we prove the existence of a Lipschitz injection $f : Z \to \ell_{p}$. Archive classification: math.FA math.GN Mathematics Subject Classification: 46C05, 46T99 Remarks: 10 pages Submitted from: westona(a)canisius.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5300 or http://arXiv.org/abs/1109.5300

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