January 2018 - Banach - mathdept.okstate.edu

Informal Analysis Seminar February 24-25, 2018
by Artem Zvavitch 05 Sep '19

05 Sep '19

Dear Colleagues, 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, February 24-25. The seminar will feature plenary speakers Robert Connelly (Cornell University), and Peter Sternberg (Indiana University) 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. Further information, and an online registration form, can be found online http://www.math.kent.edu/informal We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please register before January 29, 2018. Finally, please feel free to forward this email to any colleagues or students who you think may be interested in attending. Best regards, The Kent State Analysis Group

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Abstract of a paper by Sofiya Ostrovska, Mikhail I. Ostrovskii
by Bentuo Zheng (bzheng) 02 Jan '18

02 Jan '18

This is an announcement for the paper “On embeddings of locally finite metric spaces into $\ell_p$” by Sofiya Ostrovska<https://arxiv.org/find/math/1/au:+Ostrovska_S/0/1/0/all/0/1>, Mikhail I. Ostrovskii<https://arxiv.org/find/math/1/au:+Ostrovskii_M/0/1/0/all/0/1>. Abstract: It is known that if finite subsets of a locally finite metric space $M$ admit $C$-bilipschitz embeddings into $\ell_p$ $(1\leq p\leq\infty)$, then for every $\epsilon>0$, the space $M$ admits a $C+\epsilon$-bilipschitz embedding into $\ell_p$. The goal of this paper is to show that for $p\neq 2, \infty$ this result is sharp in the sense that ϵ cannot be dropped out of its statement. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1712.08255

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Abstract of a paper by Fernando Albiac, José L. Ansorena
by Bentuo Zheng (bzheng) 02 Jan '18

02 Jan '18

This is an announcement for the paper “Building highly conditional quasi-greedy bases in classical Banach spaces” by Fernando Albiac<https://arxiv.org/find/math/1/au:+Albiac_F/0/1/0/all/0/1>, José L. Ansorena<https://arxiv.org/find/math/1/au:+Ansorena_J/0/1/0/all/0/1>. Abstract: It is known that for a conditional quasi-greedy basis $\mathcal{B}$ in a Banach space $\mathbb{X}$, the associated sequence $(k_m[\mathcal{B}])_{m=1}^{\infty}$ of its conditionality constants verifies the estimate $k_m[\mathcal{B}]=\mathcal{O}(\log m)$ and that if the reverse inequality $\log m=\mathcal{O}(k_m[\mathcal{B}])$ holds then $\mathbb{X}$ is non-superreflexive. However, in the existing literature one finds very few instances of non-superreflexive spaces possessing quasi-greedy basis with conditionality constants as large as possible. Our goal in this article is to fill this gap. To that end we enhance and exploit a combination of techniques developed independently, on the one hand by Garrig\'os and Wojtaszczyk in [Conditional quasi-greedy bases in Hilbert and Banach spaces, Indiana Univ. Math. J. 63 (2014), no. 4, 1017-1036] and, on the other hand, by Dilworth et al. in [On the existence of almost greedy bases in Banach spaces, Studia Math. 159 (2003), no. 1, 67-101], and craft a wealth of new examples of non-superreflexive classical Banach spaces having quasi-greedy bases $\mathcal{B}$ with $k_m[\mathcal{B}]=\mathcal{O}(\log m)$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1712.04004

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Abstract of a paper by Jesús A. Jaramillo, Sebastián Lajara, Óscar Madiedo
by Bentuo Zheng (bzheng) 02 Jan '18

02 Jan '18

This is an announcement for the paper “Inversion of nonsmooth maps between Banach spaces” by Jesús A. Jaramillo<https://arxiv.org/find/math/1/au:+Jaramillo_J/0/1/0/all/0/1>, Sebastián Lajara<https://arxiv.org/find/math/1/au:+Lajara_S/0/1/0/all/0/1>, Óscar Madiedo<https://arxiv.org/find/math/1/au:+Madiedo_O/0/1/0/all/0/1>. Abstract: We study the invertibility nonsmooth maps between infinite-dimensional Banach spaces. To this end, we introduce an analogue of the notion of pseudo-Jacobian matrix of Jeyakumar and Luc in this infinite-dimensional setting. Using this, we obtain several inversion results. In particular, we give a version of the classical Hadamard integral condition for global invertibility in this context. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1712.00565

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Abstract of a paper by Marek Cúth, Benjamin Vejnar, Ondřej Kurka
by Bentuo Zheng (bzheng) 02 Jan '18

02 Jan '18

This is an announcement for the paper “Large separated sets of unit vectors in Banach spaces of continuous functions” by Marek Cúth<https://arxiv.org/find/math/1/au:+Cuth_M/0/1/0/all/0/1>, Benjamin Vejnar<https://arxiv.org/find/math/1/au:+Vejnar_B/0/1/0/all/0/1>, Ondřej Kurka<https://arxiv.org/find/math/1/au:+Kurka_O/0/1/0/all/0/1>. Abstract: The paper is concerned with the problem whether a nonseparable $\C(K)$ space must contain a set of unit vectors whose cardinality equals to the density of $\C(K)$ such that the distances between every two distinct vectors are always greater than one. We prove that this is the case if the density is at most continuum and we prove that for several classes of $\C(K)$ spaces (of arbitrary density) it is even possible to find such a set which is $2$-equilateral; that is, the distance between every two distinct vectors is exactly $2$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1712.00478

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