Dear all,
1. A quick reminder for tomorrow’s talk. Dan Freeman is speaking.
2. Please update your zoom (Go to menu on top and click Check for updates, the new version should be 5.0.1).
3. A correction: In the last sentence of the Dan’s abstract, his collaborator Mitchell Taylor’s last name was cut off. Mitchell is a grad student at Berkeley. Apologies to Mitchell! See the abstract below.
See you tomorrow!
Bunyamin
Friday May 1st 9AM CDT (e.g., Dallas, TX time). Please join us at
https://unt.zoom.us/j/512907580
Speaker: Dan Freeman, St Louis University
Title: A Schauder basis for $L_2$ consisting of non-negative functions
Abstract. We will discuss what coordinate systems can be created for $L_p(\mathbb R)$ using only non-negative functions with $1\leq p<\infty$. In particular, we will describe the construction of a Schauder basis for $L_2(\mathbb R)$ consisting of only non-negative functions. We will conclude with a discussion of some related open problems. This is joint work with Alex Powell and Mitchell Taylor.
Dear colleague,
We would like to announce a post-doctoral position in the Department
of Mathematics of the University of São Paulo (Brazil) within the
scope of Geometry of Banach spaces. This position is for a period of 12
to 24 months and as of today must end on July 31th 2022 (we expect to
extend this deadline to January 31th 2023).
The initial date of the activities is negotiable, but preferably between
August and December 2020, and the deadline to apply is May 31th, 2020. 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 September 1, 2018 of BRL 7373,10 (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/postdoc-position-open/
Don't hesitate to contact me for additional information.
All the best, Valentin.
Dear all,
The next Banach spaces webinar is on Friday May 1st 9AM CDT (e.g., Dallas, TX time). Please join us at
https://unt.zoom.us/j/512907580
Speaker: Dan Freeman, St Louis University
Title: A Schauder basis for $L_2$ consisting of non-negative functions
Abstract. We will discuss what coordinate systems can be created for $L_p(\mathbb R)$ using only non-negative functions with $1\leq p<\infty$. In particular, we will describe the construction of a Schauder basis for $L_2(\mathbb R)$ consisting of only non-negative functions. We will conclude with a discussion of some related open problems. This is joint work with Alex Powell and Mitchell.
Upcoming schedule
May 8: Chris Gartland, UIUC
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
Dear all,
The next Banach spaces webinar is on Friday April 17th 9AM CDT (e.g., Dallas, TX time). Please join us at
https://unt.zoom.us/j/512907580
Speaker: Mikhail Ostrovskii, St John’s University
Title: Transportation cost spaces, also known as Arens-Eells spaces, Lipschitz-free spaces, Wasserstein 1 spaces, etc.
Abstract. After a brief introduction I shall talk about ℓ1-subspaces in transportation cost spaces. Results presented in this talk, mentioned in it, or related to it, can be found in joint papers with Stephen Dilworth, Seychelle Khan, Denka Kutzarova, Mutasim Mim, and Sofiya Ostrovska, see
* Lipschitz free spaces on finite metric spaces<https://arxiv.org/abs/1807.03814>
* Generalized transportation cost spaces<https://arxiv.org/abs/1902.10334>
* Isometric copies of $\ell^n_{\infty}$ and $\ell_1^n$ in transportation cost spaces on finite metric spaces<https://arxiv.org/abs/1907.01155>
* On relations between transportation cost spaces and L_1<https://arxiv.org/abs/1910.03625>
Upcoming schedule
April 24: Tomasz Kania, Czech Academy
May 1: Dan Freeman, St Louis
May 8: Chris Gartland, UIUC
May 15: Gideon Schechtman, Weizmann Institute of Science
The video of last week’s talk is available here
https://www.youtube.com/watch?v=oRij6EWzlF4&feature=youtu.be&t=32
* For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach
* For a comprehensive list of talks in all areas of maths see the website Math Seminars<https://mathseminars.org/>.
Thank you, and best regards,
Bunyamin Sari
Dear all,
The next Banach spaces webinar is on Friday April 10th 9AM CDT (e.g., Dallas, TX time). Please join us at
https://unt.zoom.us/j/512907580
Speaker: Pavlos Motakis, The University of Illinois at Urbana–Champaign
Title: Coarse Universality
Abstract. The Bourgain index is a tool that can be used to show that if a separable Banach space contains isomorphic copies of all members of a class C then it must contain isomorphic copies of all separable Banach spaces. This can be applied, e.g., to the class C of separable reflexive spaces. Notably, the embedding of each member of C does not witness the universality of X. We investigate a natural coarse analogue of this index which can be used, e.g., to show that a separable metric space that contains coarse copies of all members in certain “small" classes of metric spaces C then X contains a coarse copy of $c_0$ and thus of all separable metric spaces.
This is joint work with F. Baudier, G. Lancien, and Th. Schlumprecht.
Upcoming schedule
April 17: Mikhail Ostrovskii, St. John’s
April 24: Tomasz Kania, Czech Academy
May 1: Dan Freeman, St Louis
May 8: Chris Gartland, UIUC
The video of last week’s talk is available here https://youtu.be/3U_e0Mc25cs
For more information please visit the webinar website http://www.math.unt.edu/~bunyamin/banach
Thank you, and best regards,
Bunyamin Sari
This is an announcement for the paper “The positive polynomial Schur property in Banach lattices” by Geraldo Botelho<https://arxiv.org/search/math?searchtype=author&query=Botelho%2C+G>, José Lucas P. Luiz<https://arxiv.org/search/math?searchtype=author&query=Luiz%2C+J+L+P>.
Abstract: We study the class of Banach lattices that are positively polynomially Schur. Plenty of examples and counterexamples are provided, lattice properties of this class are proved, arbitrary $L_p(\mu)$-spaces are shown to be positively polynomially Schur, lattice analogues of results on Banach spaces are obtained and relationships with the positive Schur and the weak Dunford-Pettis properties are established.
https://arxiv.org/abs/2003.11626
This is an announcement for the paper ``The number of closed ideals in $L(L_p)$” by William B. Johnson<https://arxiv.org/search/math?searchtype=author&query=Johnson%2C+W+B>, Gideon Schechtman<https://arxiv.org/search/math?searchtype=author&query=Schechtman%2C+G>.
Abstract: We show that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operator Ideals". The proof is quite different from other methods of producing closed ideals in the space of bounded operators on a Banach space; in particular, the ideals are not contained in the strictly singular operators and yet do not contain projections onto subspaces that are non Hilbertian. We give a criterion for a space with an unconditional basis to have $2^{2^{\aleph_0}}$ closed ideals in term of the existence of a single operator on the space with some special asymptotic properties. We then show that for $1<q<2$ the space ${\frak X}_q$ of Rosenthal, which is isomorphic to a complemented subspace of $L_q(0,1)$, admits such an operator.
https://arxiv.org/abs/2003.11414
This is an announcement for the paper “$c_{0} \widehat{\otimes}_πc_{0}\widehat{\otimes}_πc_{0}$ is not isomorphic to a subspace of $c_{0} \widehat{\otimes}_πc_{0}$ ” by R.M. Causey<https://arxiv.org/search/math?searchtype=author&query=Causey%2C+R+M>, E. Galego<https://arxiv.org/search/math?searchtype=author&query=Galego%2C+E>, C. Samuel<https://arxiv.org/search/math?searchtype=author&query=Samuel%2C+C>.
Abstract: In the present paper we prove that the $3$-fold projective tensor product of $c_0$, $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$, is not isomorphic to a subspace of $c_{0} \widehat{\otimes}_\pi c_{0}$. In particular, this settles the long-standing open problem of whether $c_{0} \widehat{\otimes}_\pi c_{0}$ is isomorphic to $c_{0} \widehat{\otimes}_\pi c_{0}\widehat{\otimes}_\pi c_{0}$. The origin of this problem goes back to Joe Diestel who mentioned it in a private communication to the authors of paper "Unexpected subspaces of tensor products" published in 2006.
https://arxiv.org/abs/2003.09878
This is an announcement for the paper “Group actions on twisted sums of Banach spaces” by Jesús M.F. Castillo<https://arxiv.org/search/math?searchtype=author&query=Castillo%2C+J+M+F>, Valentin Ferenczi<https://arxiv.org/search/math?searchtype=author&query=Ferenczi%2C+V>.
Abstract: We study bounded actions of groups and semigroups on exact sequences of Banach spaces, characterizing different type of actions in terms of commutator estimates satisfied by the quasi-linear map associated to the exact sequence. As a special and important case, actions on interpolation scales are related to actions on the exact sequence induced by the scale through the Rochberg-Weiss theory. Consequences are presented in the cases of certain non-unitarizable triangular representations of the free group on the Hilbert space, of the compatibility of complex structures on twisted sums, as well as of bounded actions on the interpolation scale of Lp-spaces. As a new fundamental example, the isometry group of Lp(0,1), p different from 2, is shown to extend as an isometry group acting on the associated Kalton-Peck space Zp. Finally we define the concept of G-splitting for exact sequences admitting the action of a semigroup G, and give criteria and examples to relate G-splitting and usual splitting of exact sequences: while both are equivalent for amenable groups and, for example, reflexive spaces, counterexamples are provided where one of these hypotheses is not satisfied.
https://arxiv.org/abs/2003.09767