February 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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Geometrical Aspects of Banach Spaces 2018, June 25-29, 2018, University of Birmingham, UK
by Olga Maleva 14 Feb '18

14 Feb '18

Dear Colleagues, Please find below a first announcement of the workshop which we hope will be of interest to you. Please feel free to forward this information further. *Geometrical Aspects of Banach Spaces 2018** **June 25-29, 2018** **University of Birmingham** **Birmingham, United Kingdom** * Main speakers: Javier Alejandro Chavez Dominguez, University of Oklahoma Gilles Godefroy, University Paris VI Sophie Grivaux, University of Lille William Johnson*, Texas A&M University David Preiss, University of Warwick Gideon Schechtman, Weizmann Institute of *TBC The homepage of the workshop is: http://tinyurl.com/banach-workshop OR http://web.mat.bham.ac.uk/O.Maleva/banach/ We invite you to register an interest in attending the workshop and contributing a talk by _*30 April 2018*_ via http://tinyurl.com/banach-workshop/reg.php or http://web.mat.bham.ac.uk/O.Maleva/banach/reg.php We expect to be able to cover some expenses (such as accommodation and local travel) for participants at an early stage of their career (PhD students, postdocs). Please indicate if you are requesting financial support during registration (use the "free comments" field). Sincerely, Olga Maleva and Jan Kolar (organisers)

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Neal Carothers
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

Dear All, I am forwarding the following sad news to you about Neal Carothers. Bentuo > Dear All, > > > > It is with a heavy heart I am sharing with you the sad news that Dr. Neal > Carothers passed away on January 29, 2018. > > > > There are not enough words to properly describe the impact Neal made on > this > department and the math community during his tenure at BGSU. It is touching > to see all of the kind words and memories shared about Neal from the math > community. Dr. Steven Seubert who was a close friend and colleague of Neal > did a good job portraying Neal’s impactful professional career. I am > honored > to have Steve’s permission to share his message about Neal with you: > > > > “It is with the greatest sadness that I have learned of the passing of Neal > Carothers. I am indebted to Neal not only on a professional, but a > personal > level as well. He was a gifted mathematician, exceptional educator, and > expositor of the highest degree. I not only learned a lot of mathematics > from > him > > (and from his book 'Real Analysis"), but learned a lot about how to > share it > with others; his love of and passion for mathematics was evident and > infectious and he had a profound effect on my career. No doubt this was > also > true for the generations of students he trained at BGSU. > > > > He amassed the usual research credentials publishing more than a dozen > refereed research articles in some of the most prestigious journals in his > field and he supervised three students who earned their PhD under his > tutelage. He was a popular speaker delivering over a dozen invited > addresses > and wrote two books. > > > > On the administrative end, Neal served the department in all of the most > important capacities, as a member of its Advisory, Personnel, and Promotion > and Tenure Committees, and from 1999-2007, as its Chair and with impressive > results. A hallmark of his leadership was to have nurtured strong graduate > programs and fostered strong relationships with departments and programs > all > across campus by his presence at the college and university levels. > > > > I am certain that one of Neal's most cherished accomplishments would be his > reputed text 'Real analysis’. I am including below a copy of one review for > this exceptional text which compares it to several other well-known > books by > some of the most revered of all mathematicians of our era. When the review > states that Neal's book 'will sit happily alongside classics such as > Apostol's Mathematical analysis, Royden's Real analysis, Rudin's Real and > complex analysis and Hewitt and Stromberg's Real and abstract analysis,' it > is acknowledging Neal as a supreme expositor and master of his trade.' > > > > You will be sorely missed, my friend.” > > > > > > > > [IMAGE] > > > > At this time, we do not have specific arrangements for the funeral, but you > might want to check any update with Dunn Funeral Home at > http://www.dunnfuneralhome.com/obituaries/Neal-L-Carothers?obId=2936577#/cel > > ebrationWall > > > RIP, Dear Neal. > > Hanfeng > > Hanfeng Chen > > Professor and Chair

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Abstract of a paper by Joanna Garbulińska-Węgrzyn
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “A note on the universal separable Banach space with an unconditional Schauder basis with constant K” by Joanna Garbulińska-Węgrzyn<https://arxiv.org/find/math/1/au:+Garbulinska_Wegrzyn_J/0/1/0/all/0/1>. Abstract: Using the technique of Fraisse theory we construct a universal object in the class of separable Banach spaces with an unconditional Schauder basis with constant $K$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.10064

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Abstract of a paper by Debmalya Sain, Kallol Paul, Arpita Mal
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “On extreme contractions between real Banach spaces” by Debmalya Sain<https://arxiv.org/find/math/1/au:+Sain_D/0/1/0/all/0/1>, Kallol Paul<https://arxiv.org/find/math/1/au:+Paul_K/0/1/0/all/0/1>, Arpita Mal<https://arxiv.org/find/math/1/au:+Mal_A/0/1/0/all/0/1>. Abstract: We completely characterize extreme contractions between two-dimensional strictly convex and smooth real Banach spaces, perhaps for the very first time. In order to obtain the desired characterization, we introduce the notions of (weakly) compatible point pair (CPP) and $\mu$−compatible point pair ($\mu$−CPP) in the geometry of Banach spaces. As a concrete application of our abstract results, we describe all rank one extreme contractions in $L(\ell_4^2, \ell_4^2)$ and $L(\ell_4^2, H)$, where ℍ is any Hilbert space. We also prove that there does not exist any rank one extreme contractions in $L(H, \ell_p^2)$, whenever $p$ is even and $H$ is any Hilbert space. We further study extreme contractions between infinite-dimensional Banach spaces and obtain some analogous results. Finally, we characterize real Hilbert spaces among real Banach spaces in terms of CPP, that substantiates our motivation behind introducing these new geometric notions. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.09980

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Abstract of a paper by Tiexin Guo, Erxin Zhang, Yachao Wang, George Yuan
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “Kirk's Fixed Point Theorem in Complete Random Normed modules” by Tiexin Guo<https://arxiv.org/find/math/1/au:+Guo_T/0/1/0/all/0/1>, Erxin Zhang<https://arxiv.org/find/math/1/au:+Zhang_E/0/1/0/all/0/1>, Yachao Wang<https://arxiv.org/find/math/1/au:+Wang_Y/0/1/0/all/0/1>, George Yuan<https://arxiv.org/find/math/1/au:+Yuan_G/0/1/0/all/0/1>. Abstract: Recently, stimulated by financial applications and $L_0$--convex optimization, Guo, et.al introduced the notion of $L_0$--convex compactness for an $L_0$--convex subset of a Hausdorff topological module over the topological algebra $L_0(P, K)$, where K is the scalar field of real or complex numbers and $L_0(P, K)$ the algebra of equivalence classes of $K$--valued measurable functions defined on a $\sigma$--finite measure space $(\omega, F, \mu)$, endowed with the topology of convergence locally in measure. A complete random normed module (briefly, RN module), as a random generalization of a Banach space, is just such a kind of topological module, this paper further introduces the notion of random normal structure and gives various kinds of determination theorems for a closed $L_0$--convex subset to have random normal structure or $L_0$--convex compactness, in particular we prove a characterization theorem for a closed $L_0$--convex subset to have $L_0$--convex compactness, which can be regarded as a generalization of the famous James characterization theorem for a closed convex subset of a Banach space to be weakly compact. Based on these preparations, we generalize the classical Kirk's fixed point theorem from a Banach space to a complete RN module as follows: Let $(E, \|\cdot\|)$ be a complete RN module and $V\subset E$ a nonempty $L_0$--convexly compact closed $L_0$--convex subset with random normal structure, then every nonexpansive self—mapping $f$ from $V$ to $V$ has a fixed point in $V$. The generalized Kirk's fixed point theorem is also of fundamental importance in random functional analysis, for example, we can derive from it a very general random fixed point theorem, which unifies and improves several known random fixed point theorems for random nonexpansive mappings. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.09341

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Abstract of a paper by C.S. Kubrusly, B.P. Duggal
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “On Weak Supercyclicity I” by C.S. Kubrusly<https://arxiv.org/find/math/1/au:+Kubrusly_C/0/1/0/all/0/1>, B.P. Duggal<https://arxiv.org/find/math/1/au:+Duggal_B/0/1/0/all/0/1>. Abstract: This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.08091

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Abstract of a paper by Elia Bruè, Simone Di Marino, Federico Stra
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “Linear Lipschitz and $C^1$ extension operators through random projection” by Elia Bruè<https://arxiv.org/find/math/1/au:+Brue_E/0/1/0/all/0/1>, Simone Di Marino<https://arxiv.org/find/math/1/au:+Marino_S/0/1/0/all/0/1>, Federico Stra<https://arxiv.org/find/math/1/au:+Stra_F/0/1/0/all/0/1>. Abstract: We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and $C^1$ functions. This way we prove more directly a result by Lee and Naor and we generalize the $C^1$ extension theorem by Whitney to Banach spaces. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.07533

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Abstract of a paper by Taras Banakh, Joanna Garbulińska-Węgrzyn
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “The universal separable Banach space with a monotone unordered basis” by Taras Banakh<https://arxiv.org/find/math/1/au:+Banakh_T/0/1/0/all/0/1>, Joanna Garbulińska-Węgrzyn<https://arxiv.org/find/math/1/au:+Garbulinska_Wegrzyn_J/0/1/0/all/0/1>. Abstract: Using the technique of Fra\"iss\'e theory we construct a universal object in the class of separable Banach spaces with normalized monotone unordered Schauder basis. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.07433

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Abstract of a paper by Antonio Avilés, Grzegorz Plebanek, José David Rodríguez Abellán
by Bentuo Zheng (bzheng) 03 Feb '18

03 Feb '18

This is an announcement for the paper “Chain conditions in free Banach lattices” by Antonio Avilés<https://arxiv.org/find/math/1/au:+Aviles_A/0/1/0/all/0/1>, Grzegorz Plebanek<https://arxiv.org/find/math/1/au:+Plebanek_G/0/1/0/all/0/1>, José David Rodríguez Abellán<https://arxiv.org/find/math/1/au:+Abellan_J/0/1/0/all/0/1>. Abstract: We show that the free Banach lattice FBL$[E]$ generated by a Banach space $E$ satisfies the countable chain condition, and if the Banach space $E$ is moreover weakly compactly generated, then FBL$[E]$ satisifes Knaster's condition $K_2$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1801.07027

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