Banach May 2020

banach@mathdept.okstate.edu

2 participants
5 discussions

Banach spaces webinar on Friday 5/29 by Miguel Martin
by Sari, Bunyamin 26 May '20

26 May '20

Dear all, The next Banach spaces webinar is on Friday May 29 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Miguel Martin (University of Granada) Title: On Quasi norm attaining operators between Banach spaces Abstract: This talk deals with a very recently introduced weakened notion of norm attainment for bounded linear operators. An operator $T\colon X \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is quasi norm attaining if there is a sequence $(x_n)$ of norm one elements in $X$ such that $(Tx_n)$ converges to some $u\in Y$ with $\|u\|=\|T\|$. Norm attaining operators in the usual sense (i.e. operators for which there is a point in the unit ball where the norm of its image equals the norm of the operator) and compact operators satisfy this definition. The main result is that strong Radon-Nikodým operators (such as weakly compact operators can be approximated by quasi norm attaining operators (even by a stronger version of the definition), a result which does not hold for norm attaining operators. This allows us to give characterizations of the Radon-Nikodým property in term of the denseness of quasi norm attaining operators for both domain spaces and range spaces, extending previous results by Bourgain and Huff. We will also present positive and negative results on the denseness of quasi norm attaining operators, characterize both finite dimensionality and reflexivity in terms of quasi norm attaining operators, discuss conditions to obtain that quasi norm attaining operators are actually norm attaining, study the relationship with the norm attainment of the adjoint operator. We will finish the talk discussing some remarks and open questions. The content of the talk is based on the recent preprint On Quasi norm attaining operators between Banach spaces by Geunsu Choi, Yun Sung Choi, Mingu Jung, and Miguel Martin. * Please note that the new website for mathseminars.org is https://researchseminars.org/, which now lists seminars also from other sciences. (If you imported talk schedules to your calendar from mathseminars, you will have to delete and redo it from the new site.) * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule June 5: Denny Leung (National University of Singapore) Thank you, and best regards, Bunyamin Sari

1 0

Banach spaces webinar on Friday 5/22 by Pedro Tradacete
by Sari, Bunyamin 18 May '20

18 May '20

Dear all, The next Banach spaces webinar is on Friday May 22 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Pedro Tradacete, Instituto de Ciencias Matemáticas Title: Free Banach Lattices Abstract. We will start recalling the construction of the free Banach lattice generated by a Banach space. This notion provides a new link betweeen Banach space and Banach lattice properties. We will show how this can be useful to tackle some problems and discuss some open questions. The material of the talk is partially based on the following papers: * The free Banach lattice generated by a Banach space by Antonio Avilés, José Rodríguez, Pedro Tradacete, J. Funct. Anal. 274 (2018), no. 10, 2955-2977<https://arxiv.org/abs/1706.08147> * The free Banach lattices generated by $\ell_p$ and $c_0$ by Antonio Avilés, Pedro Tradacete, Ignacio Villanueva, Rev.Mat. Complutense 32 (2019), no. 2, 353-364.<https://arxiv.org/abs/1806.02553> * You can add the Webinars to your calendar by clicking on attachment * For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Upcoming schedule May 29 Miguel Martin, University of Granada On Quasi norm attaining operators between Banach spaces Thank you, and best regards, Bunyamin Sari

1 0

Banach spaces webinar on Friday 5/15 by Gideon Schechtman
by Sari, Bunyamin 11 May '20

11 May '20

Dear all, The next Banach spaces webinar is on Friday May 15 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Gideon Schechtman Weizmann Institute of Science Title: The number of closed ideals in $L(L_p)$. Abstract. I intend to review what is known about the closed ideals in the Banach algebras $L(L_p(0,1))$. Then concentrate on a recent result of Bill Johnson and myself showing that for $1<p\not= 2<\infty$ there are exactly $2^{2^{\aleph_0}}$ different closed ideals in $L(L_p(0,1))$. Upcoming schedule May 22 Pedro Tradacete Instituto de Ciencias Matemáticas Free Banach Lattices For more information about the past and future talks, and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

1 0

Banach spaces webinar on Friday 5/8 by Chris Gartland
by Sari, Bunyamin 04 May '20

04 May '20

Dear all, The next Banach spaces webinar is on Friday May 8 9AM CDT (e.g., Dallas, TX time). Please join us at https://unt.zoom.us/j/512907580 Speaker: Chris Gartland, University of Illinois Urbana Champagne Title: Lipschitz Free Spaces over Locally Compact Metric Spaces Abstract. The talk is generally about questions of local-to-global phenomena in metric and Banach space theory. There are two motivating questions: Let X be a complete, locally compact metric space. (1) If every compact subset of X biLipschitz embeds into a Banach space with the Radon-Nikodym property, is the same true of X? (2) If the Lipschitz free space over K has the Radon-Nikodym property for every compact subset K of X, is the same true for the Lipschitz free space over X? We will first overview the theory of non-biLipschitz embeddability of metric spaces into Banach spaces with the Radon-Nikodym property, and then discuss an idea developed in an attempt to answer (2). We will show how this idea may be used to answer modified versions of (2) when the Radon-Nikodym property is replaced by the Schur or approximation property. Upcoming schedule May 15 Gideon Schechtman Weizmann Institute of Science May 22 Pedro Tradacete Instituto de Ciencias Matemáticas May 29 Miguel Martin University of Granada June 5 Denny Leung National University of Singapore June 12 Noé de Rancourt Kurt Gödel Research Center June 19 Christian Rosendal UIC and NSF June 26 Pete Casazza University of Missouri For more information past talks and videos please visit the webinar website http://www.math.unt.edu/~bunyamin/banach Thank you, and best regards, Bunyamin Sari

1 0

Announcement of New Papers
by Bentuo Zheng (bzheng) 04 May '20

04 May '20

Dear Subscribers, Please check the following link for updated list of papers in April, 2020. https://bentuo.wixsite.com/banach/banach-space-bulletin-board Best, Bentuo Zheng

1 0

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

2009

2008

2007

2006

2005

2004

Banach May 2020