Banach January 2016

banach@mathdept.okstate.edu

2 participants
20 discussions

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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[Banach Space Bulletin Board] Abstract of a paper by Mieczyslaw Mastylo, Gord Sinnamon
by Bentuo Zheng (bzheng) 29 Jan '16

29 Jan '16

This is an announcement for the paper "Calderon-Mityagin couples of Banach spaces related to decreasing functions” by Mieczyslaw Mastylo, Gord Sinnamon. Abstract: A number of Calderon-Mityagin couples and relative Calderon-Mityagin pairs are identified among Banach function spaces defined in terms of the least decreasing majorant construction on the half line. The interpolation structure of such spaces is shown to closely parallel that of the rearrangement invariant spaces, and it is proved that a couple of these spaces is a Calderon-Mityagin couple if and only if the corresponding couple of rearrangement invariant spaces is a Calderon-Mityagin couple. Consequently, the class of all interpolation spaces for any couple of spaces of this type admits a complete description by the K-method if and only if the class of all interpolation spaces for the corresponding couple of rearrangement invariant spaces does. Analogous results are proved for spaces defined in terms of the level function construction. In the main, the conclusions for both types of spaces remain valid when Lebesgue measure on the half line is replaced by a general Borel measure on R. However, for certain measures the class of interpolation spaces of these new spaces may be degenerate, reducing the "if and only if" of the main results to a single implication. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.06861

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[Banach Space Bulletin Board] Abstract of a paper by Antonio Aviles, Jose Rodriguez
by Bentuo Zheng (bzheng) 29 Jan '16

29 Jan '16

This is an announcement for the paper "Convex combinations of weak$^*$-convergent sequences and the Mackey topology” by Antonio Aviles, Jose Rodriguez. Abstract: A Banach space $X$ is said to have property $(K)$ if every $w^*$-convergent sequence in $X^*$ admits a convex block subsequence which converges with respect to the Mackey topology. We study the connection of this property with strongly weakly compactly generated Banach spaces and its stability under subspaces, quotients and $\ell_p$-sums. We extend a result of Frankiewicz and Plebanek by proving that property $(K)$ is preserved by $\ell_1$-sums of less than $p$ summands. Without any cardinality restriction, we show that property $(K)$ is stable under $\ell_p$-sums for $1<p<\infty$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.05825

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[Banach Space Bulletin Board] Abstract of a paper by Piotr Drygier, Grzegorz Plebanek
by Bentuo Zheng (bzheng) 29 Jan '16

29 Jan '16

This is an announcement for the paper “Caompactifications of $\omega$ and the Banach Space $c_0$ by Piotr Drygier, Grzegorz Plebanek. Abstract: We investigate for which compactifications $\gamma\omega$ of the discrete space of natural numbers $\omega$, the natural copy of the Banach space $c_0$ is complemented in $C(\gamma\omega)$. We show, in particular, that the separability of the remainder of $\gamma\omega$ is neither sufficient nor necessary for $c_0$ being complemented in $C(\gamma\omega)$ (for the latter our result is proved under the continuum hypothesis). We analyse, in this context, compactifications of $\omega$ related to embeddings of the measure algebra into $P(\omega)/fin$. We also prove that a Banach space $C(K)$ contains a rich family of complemented copies of $c_0$ whenever the compact space $K$ admits only measures of countable Maharam type. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.03770

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[Banach Space Bulletin Board] Abstract of a paper by Vyacheslav V. Chistyakov, Svetlana A. Chistyakova
by Bentuo Zheng (bzheng) 29 Jan '16

29 Jan '16

This is an announcement for the paper “The joint modulus of variation of metric space valued functions and pointwise selection principles” by Vyacheslav V. Chistyakov, Svetlana A. Chistyakova. Abstract: Given $T\subset\mathbb{R}$ and a metric space $M$, we introduce a nondecreasing sequence of pseudo metrics $\{\mu_n\}$ on $MT$ (the set of all functions from $T$ into $M$), called the joint modulus of variation. We prove that if two sequences of functions $(f_j)$ and $(g_j)$ from $MT$ are such that $(f_j)$ is pointwise precompact, $(g_j)$ is pointwise convergent, and the limit superior of $\mu_n(f_j, g_j)$ as $j\to\infty$ is $o(n)$) as $n\to\infty$, then $(f_j)$ admits a pointwise convergent subsequence whose limit is a conditionally regulated function. We illustrate the sharpness of this result by examples (in particular, the assumption on the lim sup is necessary for uniformly convergent sequences $(f_j)$ and $(g_j)$, and `almost necessary' when they converge pointwise) and show that most of the known Helly-type pointwise selection theorems are its particular cases. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.07298

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[Banach Space Bulletin Board] Abstract of a paper by Nik Weaver
by Bentuo Zheng (bzheng) 29 Jan '16

29 Jan '16

This is an announcement for the paper “A "quantum" Ramsey theorem for operator systems” by Nik Weaver. Abstract: Let V be a linear subspace of $M_n(C)$ which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim$(PVP) = 1$ or $k^2$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.01259

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[Banach Space Bulletin Board] Abstract of a paper by Jesús M. F. Castillo
by Bentuo Zheng (bzheng) 17 Jan '16

17 Jan '16

This is an announcement for the paper “Nonseparable $C(K)$-spaces can be twisted when $K$ is a finite height compact” by Jesús M. F. Castillo<http://arxiv.org/find/math/1/au:+Castillo_J/0/1/0/all/0/1>. Abstract: We show that, given a nonmetrizable compact space K having ω-derived set empty, there always exist nontrivial exact sequences 0→c0→E→C(K)→0. This partially solves a problem posed in several papers: Is Ext(C(K),c0)≠0 for K a nonmetrizable compact set? The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.02037 _______________________________________________ Banach mailing list Banach(a)mathdept.okstate.edu<mailto:Banach@mathdept.okstate.edu> http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

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[Banach Space Bulletin Board] Abstract of a paper by Jesús M. F. Castillo, Pier Luigi Papini
by Bentuo Zheng (bzheng) 17 Jan '16

17 Jan '16

This is an announcement for the paper “On isomorphically polyhedral $\mathcal{L}_{\infty}$-spaces” by Jesús M. F. Castillo<http://arxiv.org/find/math/1/au:+Castillo_J/0/1/0/all/0/1>, Pier Luigi Papini<http://arxiv.org/find/math/1/au:+Papini_P/0/1/0/all/0/1>. Abstract: We show that there exist ∞-subspaces of separable isomorphically polyhedral Lindenstrauss spaces that cannot be renormed to be a Lindenstrauss space. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.02035 _______________________________________________ Banach mailing list Banach(a)mathdept.okstate.edu<mailto:Banach@mathdept.okstate.edu> http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach.

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[Banach Space Bulletin Board] Abstract of a paper by Apostolos Giannopoulos, Labrini Hioni, Antonis Tsolomitis
by Bentuo Zheng (bzheng) 17 Jan '16

17 Jan '16

This is an announcement for the paper “Geometry of random sections of isotropic convex bodies” by Apostolos Giannopoulos<http://arxiv.org/find/math/1/au:+Giannopoulos_A/0/1/0/all/0/1>, Labrini Hioni<http://arxiv.org/find/math/1/au:+Hioni_L/0/1/0/all/0/1>, Antonis Tsolomitis<http://arxiv.org/find/math/1/au:+Tsolomitis_A/0/1/0/all/0/1>. Abstract: Let K be an isotropic symmetric convex body in ℝn. We show that a subspace F∈Gn,n−k of codimension k=γn, where γ∈(1/n√,1), satisfies K∩F⊆(cγ−1n√LK)Bn2∩F with probability greater than 1−exp(−n√). This implies that a random U∈O(n) satisfies K∩U(K)⊆(c1n√LK)Bn2 with probability greater than 1−e−n, where c1>0 is an absolute constant. Using a different method we study the same question for the Lq-centroid bodies Zq(μ) of an isotropic log-concave probability measure μ on ℝn. For every 1⩽q⩽n and γ∈(0,1) we show that a random subspace F∈Gn,γn satisfies Zq(μ)∩F⊆c2(γ)q√Bn2∩F; this implies that a random U∈O(n) satisfies Zq(μ)∩U(Zq(μ))⊆c3q√Bn2. Finally, we show that if an isotropic symmetric convex body has maximal isotropic constant then a random n/2-dimensional section K∩F of K has isotropic constant LK∩F⩽c4, where c4>0 is an absolute constant, and that K∩U(K)⊆c5n√Bn2 for a random U∈O(n). The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1601.02254 _______________________________________________ Banach mailing list Banach(a)mathdept.okstate.edu<mailto:Banach@mathdept.okstate.edu> http://cauchy.math.okstate.edu/cgi-bin/mailman/listinfo/banach

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Banach January 2016