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[Banach Space Bulletin Board] Abstract of a paper by R. M. Lochowski
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity” by R. M. Lochowski. Abstract: Using truncated variation techniques we derive a new theorem on the existence of the Riemann-Stieltjes integral driven by irregular signals in Banach spaces. Next, for any $p\geq 1$ we introduce the space of regulated functions $f: [a, b]\rightarrow W$ ($a<b$ are real numbers and $W$ is a Banach space), which may be uniformly approximated with accuracy $\delta>0$ by functions whose total variation is of order $\delta_{1-p}$ as $\delta\rightarrow 0+$. As an application of these results we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by irregular signals. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.02269

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[Banach Space Bulletin Board] Abstract of a paper by R. Chill and Yu. Tomilov
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Operators $L^1 (\mathbb R_+ )\to X$ and the norm continuity problem for semigroups” by R. Chill and Yu. Tomilov. Abstract: We present a new method for constructing $C_0$-semigroups for which properties of the resolvent of the generator and continuity properties of the semigroup in the operator-norm topology are controlled simultaneously. It allows us to show that a) there exists a $C_0$--semigroup which is continuous in the operator-norm topology for $t\in [0,1]$ such that the resolvent of its generator has a logarithmic decay at infinity along vertical lines; b) there exists a $C_0$--semigroup which is continuous in the operator-norm topology for no $t\in R_+$ such that the resolvent of its generator has a decay along vertical lines arbitrarily close to a logarithmic one. These examples rule out any possibility of characterizing norm-continuity of semigroups on arbitrary Banach spaces in terms of resolvent-norm decay on vertical lines. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.01163

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[Banach Space Bulletin Board] Abstract of a paper by D. Candeloro, L. Di Piazza, K. Musial and A. R. Sambuchini
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Gauge integrals and selections of weakly compact valued multifunctions” by D. Candeloro, L. Di Piazza, K. Musial and A. R. Sambuchini. Abstract: In the paper Henstock, McShane, Birkhoff and variationally multivalued integrals are studied for multifunctions taking values in the hyperspace of convex and weakly compact subsets of a general Banach space X. In particular the existence of selections integrable in the same sense of the corresponding multifunctions has been considered. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.00473

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Texas A&M 2016 Concentration Week: Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications
by Florent P. Baudier 14 Feb '16

14 Feb '16

Dear colleagues, Tuesday July 5- Saturday July 9, 2016 there will be a Concentration Week, "Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications", organized by Florent Baudier, Mikhail Ostrovskii, Lova Randrianarivony and Thomas Schlumprecht. The Concentration Week aims to bring together researchers in analysis on metric spaces, discrete geometry, nonlinear Banach space geometry, and geometric group theory, and to facilitate further interaction among researchers in these fields. The homepage of the Concentration Week is located at http://www.math.tamu.edu/~florent/cw2016.html For information about the Concentration Week "Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications", please contact Florent Baudier <florent at math.tamu.edu>. This concentration week is sponsored by the Workshop in Analysis and Probability at Texas A&M. You can get some information about the Workshop from the home page, URL http://www.math.tamu.edu/~kerr/workshop/ The Workshop is supported in part by grants from the National Science Foundation (NSF). Minorities, women, graduate students, and young researchers are especially encouraged to attend. For logistical support, including requests for support, please contact Cara Starmer <cara at math.tamu.edu>. For more information on the Workshop itself, please contact William Johnson <johnson at math.tamu.edu>, David Kerr <kerr at math.tamu.edu>, or Gilles Pisier <pisier at math.tamu.edu>. Sincerely, F. Baudier (Texas A&M University), for the organizing committee: M. Ostrovskii (St John's University), N. Randrianarivony (St Louis University), Th. Schlumprecht (Texas A&M University). -- Florent P. Baudier Visiting Assistant Professor Department of Mathematics Texas A&M University Office: Blocker 525C webpage : http://www.math.tamu.edu/~florent/ Mailstop 3368 | College Station, TX 77843 Fax. 979.845.6028

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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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