Banach May 2017

banach@mathdept.okstate.edu

2 participants
12 discussions

Abstract of a paper by Catalin Badea, David Seifert
by Bentuo Zheng (bzheng) 30 Apr '17

30 Apr '17

This is an announcement for the paper “Quantified asymptotic behaviour of Banach space operators and applications to iterative projection methods” by Catalin Badea<https://arxiv.org/find/math/1/au:+Badea_C/0/1/0/all/0/1>, David Seifert<https://arxiv.org/find/math/1/au:+Seifert_D/0/1/0/all/0/1>. Abstract: We present an extension of our earlier work [Ritt operators and convergence in the method of alternating projections, J. Approx. Theory, 205:133-148, 2016] by proving a general asymptotic result for orbits of an operator acting on a reflexive Banach space. This result is obtained under a condition involving the growth of the resolvent, and we also discuss conditions involving the location and the geometry of the numerical range of the operator. We then apply the general results to some classes of iterative projection methods in approximation theory, such as the Douglas-Rachford splitting method and, under suitable geometric conditions either on the ambient Banach space or on the projection operators, the method of alternating projections. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1704.00437

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Abstract of a paper by James Kilbane
by Bentuo Zheng (bzheng) 30 Apr '17

30 Apr '17

This is an announcement for the paper “On Embeddings of Finite Subsets of $\ell_p$” by James Kilbane<https://arxiv.org/find/math/1/au:+Kilbane_J/0/1/0/all/0/1>. Abstract: We study finite subsets of $\ell_p$ and show that, up to nowhere dense and Haar null complement, all of them embed isometrically into any Banach space that uniformly contains the spaces $\ell_p^n, n\in\mathbb{N}$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1704.00319

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Banach May 2017