July 2017 - Banach - mathdept.okstate.edu

Workshop in Geometry of Banach Spaces
by Bentuo Zheng (bzheng) 26 Jul '17

26 Jul '17

1st ANNOUNCEMENT OF BWB 2018 Second Brazilian Workshop in Geometry of Banach Spaces August 13-17, 2018 Maresias, Sao Paulo State, Brazil. (Satellite Conference of the ICM 2018) We are glad to announce that we are organizing the Second Brazilian Workshop in Geometry of Banach Spaces, as a satellite conference of the ICM 2018 (Rio de Janeiro). This international conference will take place at the Beach Hotel Maresias, on the coast of Sao Paulo State, in Maresias, in the week August 13-17, 2018. The scientific program will focus on the theory of geometry of Banach spaces, with emphasis on the following directions: large scale geometry of Banach spaces; nonlinear theory; homological theory and set theory. The webpage of the workshop is under construction and will be available at http://www.ime.usp.br/~banach/bwb2018/<http://www.ime.usp.br/%7Ebanach/bwb2014/> Registration will start early 2018. Additional scientific, practical and financial information will be given at that time. Plenary speakers: S. A. Argyros (Nat. Tech. U. Athens) G. Godefroy (Paris 6) S. Grivaux* (U. Picardie Jules Verne) R. Haydon* (U. Oxford) W. B. Johnson (Texas A&M) J. Lopez-Abad (U. Paris 7) A. Naor* (U. Princeton) D. Pellegrino (UFPB) G. Pisier* (Paris 6 & Texas A&M) B. Randrianantoanina (Miami U.) C. Rosendal (U. Illinois Chicago) N. Weaver (Washington U.) (* to be confirmed) Scientific committee J. M. F. Castillo (U. Extremadura) R. Deville (U. Bordeaux) V. Ferenczi (U. São Paulo) M. Gonzalez (U. Cantabria) V. Pestov (U. Ottawa & UFSC) G. Pisier (U. Paris 6 & Texas A&M) D. Preiss (U. Warwick) B. Randrianantoanina (Miami U.) We are looking forward to meeting you next year in Brazil, L. Batista, C. Brech, W. Cuellar, V. Ferenczi and P. Kaufmann

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Abstract of a paper by Casper Benjamin Freksen, Kasper Green Larsen
by Bentuo Zheng (bzheng) 17 Jul '17

17 Jul '17

This is an announcement for the paper “On Using Toeplitz and Circulant Matrices for Johnson-Lindenstrauss Transforms” by Casper Benjamin Freksen<https://arxiv.org/find/math/1/au:+Freksen_C/0/1/0/all/0/1>, Kasper Green Larsen<https://arxiv.org/find/math/1/au:+Larsen_K/0/1/0/all/0/1>. Abstract: The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that for any set of vectors $X\subset R^n$, there exists a mapping $f: X\rightarrow R^M$ such that $f(X)$ preserves all pairwise distances between vectors in $X$ to within $(1\pm\epsilon)$ if $m=O(\epsilon-2lgN)$. Much effort has gone into developing fast embedding algorithms, with the Fast Johnson-Lindenstrauss transform of Ailon and Chazelle being one of the most well-known techniques. The current fastest algorithm that yields the optimal $m=O(\epsilon-2lgN)$ dimensions has an embedding time of $m=O(nlgN+\epsilon-2lg3N)$. An exciting approach towards improving this, due to Hinrichs and Vyb\'iral, is to use a random $m\times n$ Toeplitz matrix for the embedding. Using Fast Fourier Transform, the embedding of a vector can then be computed in $O(nlgm)$ time. The big question is of course whether $m=O(\epsilon-2lgN)$ dimensions suffice for this technique. If so, this would end a decades long quest to obtain faster and faster Johnson-Lindenstrauss transforms. The current best analysis of the embedding of Hinrichs and Vyb\'iral shows that $m=O(\epsilon-2lg2N)$dimensions suffices. The main result of this paper, is a proof that this analysis unfortunately cannot be tightened any further, i.e., there exists a set of $N$ vectors requiring $m=\Omega(\epsilon-2lg2N)$for the Toeplitz approach to work. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.10110

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Abstract of a paper by Francisco L. Hernández, Evgeny M. Semenov, Pedro Tradacete
by Bentuo Zheng (bzheng) 17 Jul '17

17 Jul '17

This is an announcement for the paper “Interpolation and extrapolation of strictly singular operators between $L_p$ spaces” by Francisco L. Hernández<https://arxiv.org/find/math/1/au:+Hernandez_F/0/1/0/all/0/1>, Evgeny M. Semenov<https://arxiv.org/find/math/1/au:+Semenov_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 interpolation and extrapolation properties of strictly singular operators between different $L_p$ spaces. To this end, the structure of strictly singular non-compact operators between $L_p-L_q$ spaces is analyzed. Among other things, we clarify the relation between strict singularity and the $L$-characteristic set of an operator. In particular, Krasnoselskii's interpolation theorem for compact operators is extended to the class of strictly singular operators. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.08682

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Abstract of a paper by Antonio Avilés, José Rodríguez, Pedro Tradacete
by Bentuo Zheng (bzheng) 17 Jul '17

17 Jul '17

This is an announcement for the paper “The free Banach lattice generated by a Banach space” by Antonio Avilés<https://arxiv.org/find/math/1/au:+Aviles_A/0/1/0/all/0/1>, José Rodríguez<https://arxiv.org/find/math/1/au:+Rodriguez_J/0/1/0/all/0/1>, Pedro Tradacete<https://arxiv.org/find/math/1/au:+Tradacete_P/0/1/0/all/0/1>. Abstract: The free Banach lattice over a Banach space is introduced and analyzed. This generalizes the concept of free Banach lattice over a set of generators, and allows us to study the Nakano property and the density character of non-degenerate intervals on these spaces, answering some recent questions of B. de Pagter and A.W. Wickstead. Moreover, an example of a Banach lattice which is weakly compactly generated as a lattice but not as a Banach space is exhibited, thus answering a question of J. Diestel. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.08147

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Abstract of a paper by Teresa Bermúdez, Antonio Bonilla, Vladimir Müller, Alfredo Peris
by Bentuo Zheng (bzheng) 17 Jul '17

17 Jul '17

This is an announcement for the paper “Cesàro bounded operators in Banach spaces” by Teresa Bermúdez<https://arxiv.org/find/math/1/au:+Bermudez_T/0/1/0/all/0/1>, Antonio Bonilla<https://arxiv.org/find/math/1/au:+Bonilla_A/0/1/0/all/0/1>, Vladimir Müller<https://arxiv.org/find/math/1/au:+Muller_V/0/1/0/all/0/1>, Alfredo Peris<https://arxiv.org/find/math/1/au:+Peris_A/0/1/0/all/0/1>. Abstract: We study several notions of boundedness for operators. It is known that any power bounded operator is absolutely Ces\`aro bounded and strong Kreiss bounded (in particular, uniformly Kreiss bounded). The converses do not hold in general. In this note, we give examples of topologically mixing absolutely Ces\`aro bounded operators on $\ell_p(\mathbb{N}), 1\leq p<\infty$, which are not power bounded, and provide examples of uniformly Kreiss bounded operators which are not absolutely Ces\`aro bounded. These results complement very limited number of known examples (see \cite{Shi} and \cite{AS}). In \cite{AS} Aleman and Suciu ask if every uniformly Kreiss bounded operator $T$ on a Banach spaces satisfies that $\lim_n\|T_n/n\|=0$. We solve this question for Hilbert space operators and, moreover, we prove that, if $T$ is absolutely Ces\`aro bounded on a Banach (Hilbert) space, then $\|T_n\|=o(n)$ ($\|T_n\|=o(n^{1/2})$, respectively). As a consequence, every absolutely Ces\`aro bounded operator on a reflexive Banach space is mean ergodic, and there exist mixing mean ergodic operators on $\ell_p(\mathbb{N}), 1< p<\infty$. Finally, we give new examples of weakly ergodic $3$-isometries and study numerically hypercyclic $m$-isometries on finite or infinite dimensional Hilbert spaces. In particular, all weakly ergodic strict $3$-isometries on a Hilbert space are weakly numerically hypercyclic. Adjoints of unilateral forward weighted shifts which are strict $m$-isometries on $\ell_2(\mathbb{N})$ are shown to be hypercyclic. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.03638

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Abstract of a paper by Valentino Magnani, Andrea Pinamonti, Gareth Speight.
by Bentuo Zheng (bzheng) 17 Jul '17

17 Jul '17

This is an announcement for the paper “Porosity and Differentiability of Lipschitz Maps from Stratified Groups to Banach Homogeneous Groups” by Valentino Magnani<https://arxiv.org/find/math/1/au:+Magnani_V/0/1/0/all/0/1>, Andrea Pinamonti<https://arxiv.org/find/math/1/au:+Pinamonti_A/0/1/0/all/0/1>, Gareth Speight<https://arxiv.org/find/math/1/au:+Speight_G/0/1/0/all/0/1>. Abstract: Let $f$ be a Lipschitz map from a subset $A$ of a stratified group to a Banach homogeneous group. We show that directional derivatives of $f$ act as homogeneous homomorphisms at density points of $A$ outside a $sigma$-porous set. At density points of $A$ we establish a pointwise characterization of differentiability in terms of directional derivatives. We use these new results to obtain an alternate proof of almost everywhere differentiability of Lipschitz maps from subsets of stratified groups to Banach homogeneous groups satisfying a suitably weakened Radon-Nikodym property. As a consequence we also get an alternative proof of Pansu's Theorem. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1706.01782

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SUMIRFAS at Texas A&M
by Bill Johnson 11 Jul '17

11 Jul '17

The 2017 Summer Informal Regional Functional Analysis Seminar (SUMIRFAS) will take place July 21-23 as part of the annual Workshop in Analysis and Probability at Texas A&M University. SUMIRFAS is an annual three-day conference that aims to cover a broad spectrum of topics in analysis and probability. It is one of the peaks of activity in the Workshop every summer. Although nominally a regional seminar, the conference has grown into an international event. More information can be found at: http://www.math.tamu.edu/~kerr/workshop/sumirfas2017 Preceding SUMIRFAS next week will be the Concentration Week "Probabilistic and Algebraic Methods in Quantum Information Theory". Details can be found via the Workshop homepage at http://www.math.tamu.edu/~kerr/workshop

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1st announcement of BWB 2018
by valentin ferenczi 05 Jul '17

05 Jul '17

1st ANNOUNCEMENT OF BWB 2018 Second Brazilian Workshop in Geometry of Banach Spaces August 13-17, 2018 Maresias, Sao Paulo State, Brazil. (Satellite Conference of the ICM 2018) We are glad to announce that we are organizing the Second Brazilian Workshop in Geometry of Banach Spaces, as a satellite conference of the ICM 2018 (Rio de Janeiro). This international conference will take place at the Beach Hotel Maresias, on the coast of Sao Paulo State, in Maresias, in the week August 13-17, 2018. The scientific program will focus on the theory of geometry of Banach spaces, with emphasis on the following directions: large scale geometry of Banach spaces; nonlinear theory; homological theory and set theory. The webpage of the workshop is under construction and will be available at http://www.ime.usp.br/~banach/bwb2018/ <http://www.ime.usp.br/%7Ebanach/bwb2014/> Registration will start early 2018. Additional scientific, practical and financial information will be given at that time. Plenary speakers: S. A. Argyros (Nat. Tech. U. Athens) G. Godefroy (Paris 6) S. Grivaux* (U. Picardie Jules Verne) R. Haydon* (U. Oxford) W. B. Johnson (Texas A&M) J. Lopez-Abad (U. Paris 7) A. Naor* (U. Princeton) D. Pellegrino (UFPB) G. Pisier* (Paris 6 & Texas A&M) B. Randrianantoanina (Miami U.) C. Rosendal (U. Illinois Chicago) N. Weaver (Washington U.) (* to be confirmed) Scientific committee J. M. F. Castillo (U. Extremadura) R. Deville (U. Bordeaux) V. Ferenczi (U. São Paulo) M. Gonzalez (U. Cantabria) V. Pestov (U. Ottawa & UFSC) G. Pisier (U. Paris 6 & Texas A&M) D. Preiss (U. Warwick) B. Randrianantoanina (Miami U.) We are looking forward to meeting you next year in Brazil, L. Batista, C. Brech, W. Cuellar, V. Ferenczi and P. Kaufmann

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