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Abstract of a paper by Osamu Hatori, Shiho Oi
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper Isometries on Banach algebras of vector-valued maps” by Osamu Hatori<https://arxiv.org/find/math/1/au:+Hatori_O/0/1/0/all/0/1>, Shiho Oi<https://arxiv.org/find/math/1/au:+Oi_S/0/1/0/all/0/1>. Abstract: One of the purposes of this paper is to propose a unified approach for studies on isometries on the algebras of Lipschitz maps and continuously differentiable maps. We describe isometries on a certain admissible quadruple which is a common generalization of the algebra of Lipschitz maps and the algebra of continuously differentiable maps with values in unital commutative $C^*$-algebras. It implies that the isometry in Example 8 in \cite{jp} is indeed canonical. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.05782

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Abstract of a paper by Miroslav Bacak, Ulrich Kohlenbach
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “On proximal mappings with Young functions in uniformly convex Banach spaces” by Miroslav Bacak<https://arxiv.org/find/math/1/au:+Bacak_M/0/1/0/all/0/1>, Ulrich Kohlenbach<https://arxiv.org/find/math/1/au:+Kohlenbach_U/0/1/0/all/0/1>. Abstract: It is well known in convex analysis that proximal mappings on Hilbert spaces are $1$-Lipschitz. In the present paper we show that proximal mappings on uniformly convex Banach spaces are uniformly continuous on bounded sets. Moreover, we introduce a new general proximal mapping whose regularization term is given as a composition of a Young function and the norm, and formulate our results at this level of generality. It is our aim to obtain the corresponding modulus of uniform continuity explicitly in terms of a modulus of uniform convexity of the norm and of moduli witnessing properties of the Young function. We also derive several quantitative results on uniform convexity, which may be of interest on their own. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.04700

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Abstract of a paper by T. Domínguez Benavides, M. A, Japón
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “Komlós' Theorem and the Fixed Point Property for affine mappings” by T. Domínguez Benavides<https://arxiv.org/find/math/1/au:+Benavides_T/0/1/0/all/0/1>, M. A<https://arxiv.org/find/math/1/au:+A_M/0/1/0/all/0/1>, Japón<https://arxiv.org/find/math/1/au:+Jap%5C%27on/0/1/0/all/0/1>. Abstract: Assume that $X$ is a Banach space of measurable functions for which Koml\'os' Theorem holds. We associate to any closed convex bounded subset $C$ of $X$ a coefficient $t(C)$which attains its minimum value when $C$ is closed for the topology of convergence in measure and we prove some fixed point results for affine Lipschitzian mappings, depending on the value of $t(C)\in {1, 2]$and the value of the Lipschitz constants of the iterates. As a first consequence, for every $L<2$, we deduce the existence of fixed points for affine uniformly $L$-Lipschitzian mappings defined on the closed unit ball of $L_1([0,1])$. Our main theorem also provides a wide collection of convex closed bounded sets in $L_1([0,1])$ and in some other spaces of functions, which satisfy the fixed point property for affine nonexpansive mappings. Furthermore, this property is still preserved by equivalent renormings when the Banach-Mazur distance is small enough. In particular, we prove that the failure of the fixed point property for affine nonexpansive mappings in $L_1(\mu)$ can only occur in the extremal case $t(C)=2$. Examples are displayed proving that our fixed point theorem is optimal in terms of the Lipschitz constants and the coefficient $t(C)$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.03333

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Abstract of a paper by Elói Medina Galego, Vinícius Morelli Cortes
by Bentuo Zheng (bzheng) 03 Oct '17

03 Oct '17

This is an announcement for the paper “When does $C(K, X)$ contain a complemented copy of $c_0(\Gamma)$ iff $X$ does?” by Elói Medina Galego<https://arxiv.org/find/math/1/au:+Galego_E/0/1/0/all/0/1>, Vinícius Morelli Cortes<https://arxiv.org/find/math/1/au:+Cortes_V/0/1/0/all/0/1>. Abstract: Let $K$ be a compact Hausdorff space with weight $w(K)$, $\tau$ an infinite cardinal with cofinality $cf(\tau)>w(K)$ and $X$ a Banach space. In contrast with a classical theorem of Cembranos and Freniche it is shown that if $cf(\tau)>w(K)$ then the space $C(K, X)$ contains a complemented copy of $c_0(\Gamma)$ if and only if $X$ does. This result is optimal for every infinite cardinal $\tau$, in the sense that it can not be improved by replacing the inequality $cf(\tau)>w(K)$ by another weaker than it. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1709.01114

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Announcement of a post-doctoral position at the University of São Paulo
by valentin ferenczi 11 Sep '17

11 Sep '17

Dear colleague, We would like to announce a post-doctoral position in the Departament of Mathematics of the University of São Paulo (Brazil) within the scope of Geometry of Banach spaces. This position is for a period of 24 months (with possibility of extending the duration by 12 or 24 more months); the initial date of the activities is negotiable, but preferably between March and September 2018, and the deadline to apply is November 30th, 2017. The position is available as part of the FAPESP Thematic Project "Geometry of Banach spaces": https://geometryofbanachspaces.wordpress.com/ The position has no teaching duties and includes a monthly stipend which is, as of August 1, 2017 of BRL 7170 (tax free). It also includes partial support for travel and the first expenses upon arrival, as well as Research Contigency Funds equivalent to 15% of the fellowship. All relevant information may be found at https://geometryofbanachspaces.wordpress.com/post-doctoral-position/ We kindly ask you to forward this message to anyone you know that might be interested in this position. Best regards, Valentin Ferenczi.

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Abstract of a paper by Ahmed Youssfi, Youssef Ahmida
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “Some approximation results in Musielak-Orlicz spaces” by Ahmed Youssfi<https://arxiv.org/find/math/1/au:+Youssfi_A/0/1/0/all/0/1>, Youssef Ahmida<https://arxiv.org/find/math/1/au:+Ahmida_Y/0/1/0/all/0/1>. Abstract: We give sufficient conditions for the continuity in norm of the translation operator in the Musielak-Orlicz LM spaces. An application to the convergence in norm of approximate identities is given, whereby we prove density results of the smooth functions in LM, in both modular and norm topologies. These density results are then applied to obtain basic topological properties. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.02453

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Abstract of a paper by Antonio Jiménez-Vargas, Antonio Morales Campoy, Antonio M. Peralta, María Isabel Ramírez
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “The Mazur-Ulam property for the space of complex null sequences” by Antonio Jiménez-Vargas<https://arxiv.org/find/math/1/au:+Jimenez_Vargas_A/0/1/0/all/0/1>, Antonio Morales Campoy<https://arxiv.org/find/math/1/au:+Campoy_A/0/1/0/all/0/1>, Antonio M. Peralta<https://arxiv.org/find/math/1/au:+Peralta_A/0/1/0/all/0/1>, María Isabel Ramírez<https://arxiv.org/find/math/1/au:+Ramirez_M/0/1/0/all/0/1>. Abstract: Given an infinite set $\Gamma$, we prove that the space of complex null sequences $c_0(\Gamma)$ satisfies the Mazur-Ulam property, that is, for each Banach space $X$, every surjective isometry from the unit sphere of $c_0(\Gamma)$ onto the unit sphere of $X$ admits a (unique) extension to a surjective real linear isometry from $c_0(\Gamma)$ to $X$. We also prove that the same conclusion holds for the finite dimensional space $\ell_{\infty}^m$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.08538

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Abstract of a paper by Jesús M. F. Castillo, Yolanda Moreno
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “1-complemented subspaces of Banach spaces of universal disposition” by Jesús M. F. Castillo<https://arxiv.org/find/math/1/au:+Castillo_J/0/1/0/all/0/1>, Yolanda Moreno<https://arxiv.org/find/math/1/au:+Moreno_Y/0/1/0/all/0/1>. Abstract: We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) $\mathcal{N}$-injectivity --- in the notion of $(\alpha,\beta)$-injectivity $(\alpha,\beta)_{\lambda}$-injectivity if the parameter $\lambda$ has to be specified). Then, extend the notion of space of universal disposition to space of universal $(\alpha,\beta)$-disposition. Finally, we characterize the 1-complemented subspaces of spaces of universal $(\alpha,\beta)$-disposition as precisely the spaces $(\alpha,\beta)_1$-injective. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.03823

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Abstract of a paper by Enrique A. Sánchez-Pérez, Pedro Tradacete
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “$(p,q)$-regular operators between Banach lattices” by Enrique A. Sánchez-Pérez<https://arxiv.org/find/math/1/au:+Sanchez_Perez_E/0/1/0/all/0/1>, Pedro Tradacete<https://arxiv.org/find/math/1/au:+Tradacete_P/0/1/0/all/0/1>. Abstract: We study the class of $(,p,q)$-regular operators between quasi-Banach lattices. In particular, a representation of this class as the dual of a certain tensor norm for Banach lattices is given. We also provide some factorization results for $(p,q)$-regular operators yielding new Marcinkiewicz-Zygmund type inequalities for Banach function spaces. An extension theorem for $(q, \infty)$-regular operators defined on a subspace of $L_q$is also given. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.03363

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Abstract of a paper by Jesús M. F. Castillo, Yolanda Moreno
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “Banach and quasi-Banach spaces of almost universal complemented disposition” by Jesús M. F. Castillo<https://arxiv.org/find/math/1/au:+Castillo_J/0/1/0/all/0/1>, Yolanda Moreno<https://arxiv.org/find/math/1/au:+Moreno_Y/0/1/0/all/0/1>. Abstract: We introduce and study the notion of space of almost universal complemented disposition (a.u.c.d.) and show the existence of separable a.u.c.d. spaces with and without a Finite Dimensional Decomposition. We show that all a.u.c.d. spaces with $1$-FDD are isometric and contain isometric $1$-complemented copies of every separable Banach space with $1$-FDD. Both assertions fail without the FDD assumption. We then study spaces of universal complemented disposition (u.c.d.) and provide different constructions for such spaces. We also consider spaces of u.c.d. with respect to separable spaces. In the last section we consider $p$-Banach versions of all previous constructions showing that there are striking differences with either the Banach case or the classical case of simple universal disposition. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.02431

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