September 2015 - 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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Informal Analysis Seminar at Kent State, November 14-15.
by Artem Zvavitch 14 Mar '16

14 Mar '16

Dear Colleague, The Analysis group at Kent State University is happy to announce a meeting of the Informal Analysis Seminar, which will be held at the Department of Mathematical Sciences at Kent State University, November 14-15, 2015. The plenary lecture series will be given by: Boaz Klartag (Tel Aviv University) and Igor Rivin (University of St. Andrews) Each speaker will deliver a four hour lecture series designed to be accessible for graduate students. Funding is available to cover the local and travel expenses of a limited number of participants. Graduate students, postdoctoral researchers, and members of underrepresented groups are particularly encouraged to apply for support. A poster session will be held for researchers to display their work. Graduate students are particularly encouraged to submit a poster. Posters can be submitted electronically in PDF format before November 6, 2015. Further information, and an online registration form, can be found online http://www.math.kent.edu/~zvavitch/informal/Informal_Analysis_Seminar/Novem… We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please, register before October 1, 2015. Please feel free to contact us at informal(a)math.kent.edu for any further information. Sincerely, Analysis Group at Kent State University

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Abstract of a paper by Santeri Miihkinen
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "Strict singularity of a Volterra-type integral operator on $H^p$" by Santeri Miihkinen. Abstract: We prove that a Volterra-type integral operator $T_gf(z) = \int_0^z f(\zeta)g'(\zeta)d\zeta, \, z \in \mathbb D,$ defined on Hardy spaces $H^p, \, 1 \le p < \infty,$ fixes an isomorphic copy of $\ell^p,$ if the operator $T_g$ is not compact. In particular, this shows that the strict singularity of the operator $T_g$ coincides with the compactness of the operator $T_g$ on spaces $H^p.$ As a consequence, we obtain a new proof for the equivalence of the compactness and the weak compactness of the operator $T_g$ on $H^1$. Archive classification: math.FA Mathematics Subject Classification: 47G10 (Primary) 30H10 (Secondary ) Remarks: 14 pages, 1 figure Submitted from: santeri.miihkinen(a)helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.08356 or http://arXiv.org/abs/1509.08356

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Abstract of a paper by Jan-David Hardtke
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "On certain Opial-type results in Ces\`aro spaces of vector-valued functions" by Jan-David Hardtke. Abstract: Given a Banach space $X$, we consider Ces\`aro spaces $\text{Ces}_p(X)$ of $X$-valued functions over the interval $[0,1]$, where $1\leq p<\infty$. We prove that if $X$ has the Opial/uniform Opial property, then certain analogous properties also hold for $\text{Ces}_p(X)$. We also prove a result on the Opial/uniform Opial property of Ces\`aro spaces of vector-valued sequences. Archive classification: math.FA Mathematics Subject Classification: 46E40 46E30 46B20 Remarks: 15 pages, partial text overlap with arXiv:1403.2647 Submitted from: hardtke(a)math.fu-berlin.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.08097 or http://arXiv.org/abs/1509.08097

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Abstract of a paper by Niushan Gao, Vladimir G. Troitsky, and Foivos Xanthos
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "Uo-convergence and its applications to Ces\`aro means in Banach lattices" by Niushan Gao, Vladimir G. Troitsky, and Foivos Xanthos. Abstract: A net $(x_\alpha)$ in a vector lattice $X$ is said to uo-converge to $x$ if $|x_\alpha-x|\wedge u\xrightarrow{\rm o}0$ for every $u\ge 0$. In the first part of this paper, we study some functional-analytic aspects of uo-convergence. We prove that uo-convergence is stable under passing to and from regular sublattices. This fact leads to numerous applications presented throughout the paper. In particular, it allows us to improve several results in [26,27]. In the second part, we use uo-convergence to study convergence of Ces\`aro means in Banach lattices. In particular, we establish an intrinsic version of Koml\'os' Theorem, which extends the main results of [35,16,31] in a uniform way. We also develop a new and unified approach to Banach-Saks properties and Banach-Saks operators based on uo-convergence. This approach yields, in particular, short direct proofs of several results in [21,24,25]. Archive classification: math.FA Remarks: 45 pages Submitted from: foivos(a)ryerson.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.07914 or http://arXiv.org/abs/1509.07914

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Abstract of a paper by Gleb Sirotkin and Ben Wallis
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "Almost-invariant and essentially-invariant halfspaces" by Gleb Sirotkin and Ben Wallis. Abstract: In this paper we study sufficient conditions for an operator to have an almost-invariant half-space. As a consequence, we show that if $X$ is an infinite-dimensional complex Banach space then every operator $T\in\mathcal{L}(X)$ admits an essentially-invariant half-space. We also show that whenever a closed algebra of operators possesses a common AIHS, then it has a common invariant half-space as well. Archive classification: math.FA Mathematics Subject Classification: 15A03, 15A18, 15A60, 47L10, 47A10, 47A11, 47A15 Remarks: 11 pages. Keywords: functional analysis, Banach spaces, surjectivity The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.07428 or http://arXiv.org/abs/1509.07428

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Abstract of a paper by Grigory Ivanov
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "Hypomonotonicity of the normal cone and proximal smoothness" by Grigory Ivanov. Abstract: In this paper we study the properties of the normal cone to the proximally smooth set. We give the complete characterization of the proximally smooth set through the monotony properties of its normal cone in an arbitrary uniformly convex and uniformly smooth Banach space. We give the exact bounds for right-hand side in the monotonicity inequality for normal cone in terms of the moduli of smoothness and convexity of a Banach space. Archive classification: math.FA Submitted from: grigory.ivanov(a)phystech.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.06795 or http://arXiv.org/abs/1509.06795

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Abstract of a paper by Hana Krulisova
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "Quantification of Pe\l czy\'nski's property (V)" by Hana Krulisova. Abstract: A Banach space $X$ has Pe\l czy\' nski's property (V) if for every Banach space $Y$ every unconditionally converging operator $T\colon X\to Y$ is weakly compact. In 1962, Aleksander Pe\l czy\' nski showed that $C(K)$ spaces for a compact Hausdorff space $K$ enjoy the property (V), and some generalizations of this theorem have been proved since then. We introduce several possibilities of quantifying the property (V). We prove some characterizations of the introduced quantitative versions of this property, which allow us to prove a quantitative version of Pelczynski's result about $C(K)$ spaces and generalize it. Finally, we study the relationship of several properties of operators including weak compactness and unconditional convergence, and using the results obtained we establish a relation between quantitative versions of the property (V) and quantitative versions of other well known properties of Banach spaces. Archive classification: math.FA Remarks: 19 pages Submitted from: krulisova(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.06610 or http://arXiv.org/abs/1509.06610

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Abstract of a paper by Zhe-Ming Zheng and Hui-Sheng Ding
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "A note on closedness of the sum of two closed subspaces in a Banach space" by Zhe-Ming Zheng and Hui-Sheng Ding. Abstract: Let $X$ be a Banach space, and $M,N$ be two closed subspaces of $X$. We present several necessary and sufficient conditions for the closedness of $M+N$ ($M+N$ is not necessarily direct sum). Archive classification: math.FA Submitted from: dinghs(a)mail.ustc.edu.cn The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.06445 or http://arXiv.org/abs/1509.06445

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Abstract of a paper by Silouanos Brazitikos
by alspach＠math.okstate.edu 29 Sep '15

29 Sep '15

This is an announcement for the paper "Brascamp-Lieb inequality and quantitative versions of Helly's theorem" by Silouanos Brazitikos. Abstract: We provide a number of new quantitative versions of Helly's theorem. For example, we show that for every family $\{P_i:i\in I\}$ of closed half-spaces $$P_i=\{ x\in {\mathbb R}^n:\langle x,w_i\rangle \leq 1\}$$ in ${\mathbb R}^n$ such that $P=\bigcap_{i\in I}P_i$ has positive volume, there exist $s\leq \alpha n$ and $i_1,\ldots , i_s\in I$ such that $$|P_{i_1}\cap\cdots\cap P_{i_s}|\leq (Cn)^n\,|P|,$$ where $\alpha , C>0$ are absolute constants. These results complement and improve previous work of B\'{a}r\'{a}ny-Katchalski-Pach and Nasz\'{o}di. Our method combines the work of Srivastava on approximate John's decompositions with few vectors, a new estimate on the corresponding constant in the Brascamp-Lieb inequality and an appropriate variant of Ball's proof of the reverse isoperimetric inequality. Archive classification: math.FA Mathematics Subject Classification: 26D15 Submitted from: silouanb(a)math.uoa.gr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1509.05783 or http://arXiv.org/abs/1509.05783

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