Banach September 2011

banach@mathdept.okstate.edu

1 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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Abstract of a paper by Konrad J. Swanepoel and Rafael Villa
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "Maximal equilateral sets" by Konrad J. Swanepoel and Rafael Villa. Abstract: A subset of a normed space X is called equilateral if the distance between any two points is the same. Let m(X) be the smallest possible size of an equilateral subset of X maximal with respect to inclusion. We first observe that Petty's construction of a d-dimensional X of any finite dimension d >= 4 with m(X)=4 can be generalised to show that m(X\oplus_1\R)=4 for any X of dimension at least 2 which has a smooth point on its unit sphere. By a construction involving Hadamard matrices we then show that both m(\ell_p) and m(\ell_p^d) are finite and bounded above by a function of p, for all 1 <= p < 2. Also, for all p in [1,\infty) and natural numbers d there exists c=c(p,d) > 1 such that m(X) <= d+1 for all d-dimensional X with Banach-Mazur distance less than c from \ell_p^d. Using Brouwer's fixed-point theorem we show that m(X) <= d+1 for all d-\dimensional X with Banach-Mazur distance less than 3/2 from \ell_\infty^d. A graph-theoretical argument furthermore shows that m(\ell_\infty^d)=d+1. The above results lead us to conjecture that m(X) <= 1+\dim X. Archive classification: math.MG math.CO math.FA Mathematics Subject Classification: 46B20 (Primary), 46B85, 52A21, 52C17 (Secondary) Remarks: 15 pages Submitted from: konrad.swanepoel(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.5063 or http://arXiv.org/abs/1109.5063

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Abstract of a paper by Adriano Thiago Bernardino, Daniel Pellegrino and Juan B. Seoane-Sepulveda
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "Multiple $(p;q;r)$-summing polynomials and multilinear operators" by Adriano Thiago Bernardino, Daniel Pellegrino and Juan B. Seoane-Sepulveda. Abstract: The concept of absolutely $(p;q;r)$-summing linear operators is due to A. Pietsch; it is a natural extension of the classical notion of absolutely $(p;q)$-summing operators. Very recently D. Achour introduced the concept of absolutely $(p;q;r)$-summing multilinear mappings. In this paper we obtain some properties of this class and show that the polynomial version of this notion is neither coherent nor compatible (according to the definition of Carando, Dimant, and Muro). Here we shall provide an alternative approach that generates coherent and compatible ideals. 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/1109.4898 or http://arXiv.org/abs/1109.4898

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Abstract of a paper by Parcet Javier, Soria Fernando, and Xu Quanhua
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "On the growth of vector-valued Fourier series" by Parcet Javier, Soria Fernando, and Xu Quanhua. Abstract: We prove the 'little Carleson theorem' on the growth of Fourier series for functions taking values in a UMD Banach space. Archive classification: math.CA math.FA Submitted from: javier.parcet(a)icmat.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.4313 or http://arXiv.org/abs/1109.4313

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Abstract of a paper by Sergo A. Episkoposian
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "On greedy algorithms with respect to generalized Walsh system" by Sergo A. Episkoposian. Abstract: In this paper we proof that there exists a function f(x) belongs to L^1[0,1] such that a greedy algorithm with regard to generalized Walsh system does not converge to f(x) in L^1[0,1] norm, i.e. the generalized Walsh system is not a quasi-greedy basis in its linear span L^1[0,1]. Archive classification: math.FA Mathematics Subject Classification: 42C10, 46E30 Submitted from: sergoep(a)ysu.am The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.3806 or http://arXiv.org/abs/1109.3806

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Abstract of a paper by Sergo A. Episkoposian
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "On the existence of universal series by trigonometric system" by Sergo A. Episkoposian. Abstract: In this paper we prove the following: let $\omega(t)$ be a continuous function, increasing in $[0,\infty)$ and $\omega(+0)=0$. Then there exists a series of the form $$\sum_{k=-\infty}^\infty C_ke^{ikx} \ \ with \ \ \sum_{k=-\infty}^\infty C^2_k \omega(|C_k|)<\infty ,\ \ C_{-k}=\overline{C}_k, \eqno$$ with the following property: for each $\varepsilon>0$ a weighted function $\mu(x), 0<\mu(x) \le1, \left | \{ x\in[0,2\pi]: \mu(x)\not =1 \} \right | <\varepsilon $ can be constructed, so that the series is universal in the weighted space $L_\mu^1[0,2\pi]$ with respect to rearrangements. Archive classification: math.FA Mathematics Subject Classification: 42A20 Submitted from: sergoep(a)ysu.am The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.3805 or http://arXiv.org/abs/1109.3805

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Abstract of a paper by Dario Cordero-Erausquin and Boaz Klartag
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "Interpolations, convexity and geometric inequalities" by Dario Cordero-Erausquin and Boaz Klartag. Abstract: We survey some interplays between spectral estimates of H\"ormander-type, degenerate Monge-Amp\`ere equations and geometric inequalities related to log-concavity such as Brunn-Minkowski, Santal\'o or Busemann inequalities. Archive classification: math.FA math.CV Submitted from: cordero(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.3652 or http://arXiv.org/abs/1109.3652

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Abstract of a paper by Gilles Pisier
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "Real interpolation between row and column spaces" by Gilles Pisier. Abstract: We give an equivalent expression for the $K$-functional associated to the pair of operator spaces $(R,C)$ formed by the rows and columns respectively. This yields a description of the real interpolation spaces for the pair $(M_n(R), M_n(C))$ (uniformly over $n$). More generally, the same result is valid when $M_n$ (or $B(\ell_2)$) is replaced by any semi-finite von~Neumann algebra. We prove a version of the non-commutative Khintchine inequalities (originally due to Lust--Piquard) that is valid for the Lorentz spaces $L_{p,q}(\tau)$ associated to a non-commutative measure $\tau$, simultaneously for the whole range $1\le p,q< \infty$, regardless whether $p<2 $ or $p>2$. Actually, the main novelty is the case $p=2,q\not=2$. We also prove a certain simultaneous decomposition property for the operator norm and the Hilbert-Schmidt one. Archive classification: math.OA Mathematics Subject Classification: 47B10 Submitted from: pisier(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.1860 or http://arXiv.org/abs/1109.1860

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Abstract of a paper by Alistair Bird, Graham Jameson and Niels Jakob Laustsen
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "The Giesy--James theorem for general index $p$, with an application to operator ideals on the $p$th James space" by Alistair Bird, Graham Jameson and Niels Jakob Laustsen. Abstract: A theorem of Giesy and James states that $c_0$ is finitely representable in James' quasi-reflexive Banach space $J_2$. We extend this theorem to the $p$th quasi-reflexive James space $J_p$ for each $p \in (1,\infty)$. As an application, we obtain a new closed ideal of operators on $J_p$, namely the closure of the set of operators that factor through the complemented subspace $(\ell_\infty^1 \oplus \ell_\infty^2 \oplus \cdots \oplus \ell_\infty^n \oplus \cdots)_{\ell_p}$ of $J_p$. Archive classification: math.FA math.OA Mathematics Subject Classification: 46B45, 47L20 (Primary) 46B07, 46H10, 47L10 (Secondary) Remarks: 16 pages Submitted from: alistairbird(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.1776 or http://arXiv.org/abs/1109.1776

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Abstract of a paper by Gilles Pisier
by alspach＠math.okstate.edu 29 Sep '11

29 Sep '11

This is an announcement for the paper "Real interpolation and transposition of certain function spaces" by Gilles Pisier. Abstract: Our starting point is a lemma due to Varopoulos. We give a different proof of a generalized form this lemma, that yields an equivalent description of the $K$-functional for the interpolation couple $(X_0,X_1)$ where $X_0=L_{p_0,\infty}(\mu_1; L_q(\mu_2))$ and $X_1=L_{p_1,\infty}(\mu_2; L_q(\mu_1))$ where $0<q<p_0,p_1\le \infty$ and $(\Omega_1,\mu_1), (\Omega_2,\mu_2)$ are arbitrary measure spaces. When $q=1$, this implies that the space $(X_0,X_1)_{\theta,\infty}$ ($0<\theta<1$) can be identified with a certain space of operators. We also give an extension of the Varopoulos Lemma to pairs (or finite families) of conditional expectations that seems of independent interest. The present paper is motivated by non-commutative applications that we choose to publish separately. Archive classification: math.FA Submitted from: pisier(a)math.jussieu.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1109.1006 or http://arXiv.org/abs/1109.1006

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Banach September 2011