Banach September 2017

banach@mathdept.okstate.edu

2 participants
9 discussions

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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Abstract of a paper by Antti Rasila, Jarno Talponen, Xiaohui Zhang
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “Observations on quasihyperbolic geometry modeled on Banach spaces” by Antti Rasila<https://arxiv.org/find/math/1/au:+Rasila_A/0/1/0/all/0/1>, Jarno Talponen<https://arxiv.org/find/math/1/au:+Talponen_J/0/1/0/all/0/1>, Xiaohui Zhang<https://arxiv.org/find/math/1/au:+Zhang_X/0/1/0/all/0/1>. Abstract: In this paper, we continue our study of quasihyperbolic metric in Banach spaces. The main results of the paper present a criterion for smoothness of geodesics of quasihyperbolic type metrics in Banach spaces, under a Dini type condition on the weight function, which improves an earlier result of the two first authors. We also answer to a question posed by the two first authors in an earlier paper with R. Kl\'en, and present results related to the question on smoothness of quasihyperbolic balls. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.02240

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Abstract of a paper by James Kilbane, Mikhail I. Ostrovsk
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “There is no finitely isometric Krivine's theorem” by James Kilbane<https://arxiv.org/find/math/1/au:+Kilbane_J/0/1/0/all/0/1>, Mikhail I. Ostrovsk<https://arxiv.org/find/math/1/au:+Ostrovskii_M/0/1/0/all/0/1>. Abstract: We prove that for every $p\in (1, \infty)$, $p\neq 2$, there exist a Banach space $X$ isomorphic to $\ell_p$ and a finite subset $U$ in $\ell_p$, such that $U$ is not isometric to a subset of $X$. This result shows that the finite isometric version of the Krivine theorem (which would be a strengthening of the Krivine theorem (1976)) does not hold. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.01570

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Abstract of a paper by P.M. BernáK. Keryan, M. Passenbrunner
by Bentuo Zheng (bzheng) 01 Sep '17

01 Sep '17

This is an announcement for the paper “Unconditionality of Periodic Orthonormal Spline Systems in $L^p$” by P.M. Berná<https://arxiv.org/find/math/1/au:+Berna_P/0/1/0/all/0/1>K. Keryan<https://arxiv.org/find/math/1/au:+Keryan_K/0/1/0/all/0/1>, M. Passenbrunner<https://arxiv.org/find/math/1/au:+Passenbrunner_M/0/1/0/all/0/1>. Abstract: Given any natural number $k$ and any dense point sequence $(t_n)$ on the torus $\mathbb{T}$, we prove that the corresponding periodic orthonormal spline system of order $k$ is an unconditional basis in $L^p$ for $1<p<\infty$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1708.09294

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Banach September 2017