January 2013 - Banach - mathdept.okstate.edu

INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL (March 20-21, 2010)
by Artem Zvavitch 20 Aug '16

20 Aug '16

Dear Friends, On Saturday - Sunday, March 20-21, 2010, (best arrival date Friday, March 19/ Departure Monday, March 22) the Department of Mathematical Sciences at Kent State University will be famous but still very informal. We are happy to announce an: INFORMAL ANALYSIS SEMINAR DEDICATED TO THE WORK OF JOE DIESTEL The following people are among speakers: Peter Casazza, Hans Jarchow, Alexander Koldobsky, Pepe Orihuela, Olek Pelczynski, Thomas Schlumprecht, Lutz Weis. It would be great if you could visit Kent State and participate in the seminar! The conference will have a registration fee of $200 WHICH INCLUDES: pick up/drop off from the airport, THREE DAY STAY in the Microtel hotel at Streetsboro, Saturday/Sunday lunches/dinners to be provided at the department. If you plan to stay fewer than 3 nights or prefer to make your own accommodation arrangements, please reduce your registration fee by $45 per day that you will not use our hotel arrangements. If possible, please send a check for your registration fee, made out to the Department of Mathematical Sciences, Kent State University. The check should be mailed to Virginia Wright, Department of Mathematical Sciences, Kent State University, Kent, OH, 44242. The fee can be also be paid during the registration (check/cash). The conference is supported by NSF; The Department of Mathematical Sciences and Kent State University. Depending on funds availability the fee may be waived for young researchers and people without available funding. Please, write as soon as possible to zvavitch(a)math.kent.edu May we ask you to respond as soon as February 19 (zvavitch(a)math.kent.edu) so that we can gauge the need for housing, lecture room(s), etc. Best Regards, Analysis group at Kent State!

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Abstract of a paper by Balint Farkas
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "A Bohl--Bohr--Kadets type theorem characterizing Banach spaces not containing $c_0$" by Balint Farkas. Abstract: We prove that a separable Banach space $E$ does not contain a copy of the space $\co$ of null-sequences if and only if for every doubly power-bounded operator $T$ on $E$ and for every vector $x\in E$ the relative compactness of the sets $\{T^{n+m}x-T^nx: n\in \NN\}$ (for some/all $m\in\NN$, $m\geq 1$) and $\{T^nx:n\in \NN\}$ are equivalent. With the help of the Jacobs--de Leeuw--Glicksberg decomposition of strongly compact semigroups the case of (not necessarily invertible) power-bounded operators is also handled. Archive classification: math.FA Mathematics Subject Classification: 47A99, 46B04, 43A60 Submitted from: farkasb(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6250 or http://arXiv.org/abs/1301.6250

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Abstract of a paper by Sophie Grivaux and Maria Roginskaya
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "On Read's type operators on Hilbert spaces" by Sophie Grivaux and Maria Roginskaya. Abstract: Using Read's construction of operators without non-trivial invariant subspaces/subsets on $\ell_{1}$ or $c_{0}$, we construct examples of operators on a Hilbert space whose set of hypercyclic vectors is ``large'' in various senses. We give an example of an operator such that the closure of every orbit is a closed subspace, and then, answering a question of D. Preiss, an example of an operator such that the set of its non-hypercyclic vectors is Gauss null. This operator has the property that it is orbit-unicellular, i.e. the family of the closures of its orbits is totally ordered. We also exhibit an example of an operator on a Hilbert space which is not orbit-reflexive. Archive classification: math.FA Citation: Int. Math. Res. Not., 2008 Art. ID rnn083, 42 pp Remarks: This is a preprint version of the article "On Read's type The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6226 or http://arXiv.org/abs/1301.6226

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Abstract of a paper by Sophie Grivaux and Maria Roginskaya
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "An example of a minimal action of the free semi-group $\F^{+}_{2}$ on the Hilbert space" by Sophie Grivaux and Maria Roginskaya. Abstract: The Invariant Subset Problem on the Hilbert space is to know whether there exists a bounded linear operator $T$ on a separable infinite-dimensional Hilbert space $H$ such that the orbit $\{T^{n}x;\ n\ge 0\}$ of every non-zero vector $x\in H$ under the action of $T$ is dense in $H$. We show that there exists a bounded linear operator $T$ on a complex separable infinite-dimensional Hilbert space $H$ and a unitary operator $V$ on $H$, such that the following property holds true: for every non-zero vector $x\in H$, either $x$ or $Vx$ has a dense orbit under the action of $T$. As a consequence, we obtain in particular that there exists a minimal action of the free semi-group with two generators $\F^{+}_{2}$ on a complex separable infinite-dimensional Hilbert space $H$. Archive classification: math.FA math.DS Remarks: 10 p Submitted from: grivaux(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6144 or http://arXiv.org/abs/1301.6144

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Abstract of a paper by Sophie Grivaux and Maria Roginskaya
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "A general approach to Read's type constructions of operators without non-trivial invariant closed subspaces" by Sophie Grivaux and Maria Roginskaya. Abstract: We present a general method for constructing operators without non-trivial invariant closed subsets on a large class of non-reflexive Banach spaces. In particular, our approach unifies and generalizes several constructions due to Read of operators without non-trivial invariant subspaces on the spaces $\ell_{1}$, $c_{0}$ or $\oplus_{\ell_{2}}J$, and without non-trivial invariant subsets on $\ell_{1}$. We also investigate how far our methods can be extended to the Hilbertian setting, and construct an operator on a quasireflexive dual Banach space which has no non-trivial $w^{*}$-closed invariant subspace. Archive classification: math.FA Remarks: 62 p Submitted from: grivaux(a)math.univ-lille1.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6143 or http://arXiv.org/abs/1301.6143

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Abstract of a paper by Marek Cuth
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "Noncommutative Valdivia compacta" by Marek Cuth. Abstract: We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space K, we show that K is Corson if and only if every continuous image of K has a retractional skeleton. Archive classification: math.FA Mathematics Subject Classification: 46B26, 54D30 Submitted from: cuthm5am(a)karlin.mff.cuni.cz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.5799 or http://arXiv.org/abs/1301.5799

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Abstract of a paper by G. Garrigos and P. Wojtaszczyk
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "Conditional quasi-greedy bases in Hilbert and Banach spaces" by G. Garrigos and P. Wojtaszczyk. Abstract: We show that, for quasi-greedy bases in Hilbert spaces, the associated conditionality constants grow at most as $O(\log N)^{1-\epsilon}$, for some $\epsilon>0$, answering a question by Temlyakov. We show the optimality of this bound with an explicit construction, based on a refinement of the method of Olevskii. This construction leads to other examples of quasi-greedy bases with large $k_N$ in Banach spaces, which are of independent interest. Archive classification: math.FA math.CA Submitted from: gustavo.garrigos(a)uam.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.4844 or http://arXiv.org/abs/1301.4844

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Abstract of a paper by Florence Lancien and Christian Le Merdy
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "On functional calculus properties of Ritt operators" by Florence Lancien and Christian Le Merdy. Abstract: We compare various functional calculus properties of Ritt operators. We show the existence of a Ritt operator T : X --> X on some Banach space X with the following property: T has a bounded $\H^\infty$ functional calculus with respect to the unit disc $\D$ (that is, T is polynomially bounded) but T does not have any bounded $\H^\infty$ functional calculus with respect to a Stolz domain of $\D$ with vertex at 1. Also we show that for an R-Ritt operator, the unconditional Ritt condition of Kalton-Portal is equivalent to the existence of a bounded $\H^\infty$ functional calculus with respect to such a Stolz domain. Archive classification: math.FA math.OA Mathematics Subject Classification: 47A60 Submitted from: clemerdy(a)univ-fcomte.fr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.4875 or http://arXiv.org/abs/1301.4875

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Abstract of a paper by Yousef Estaremi
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "Multiplication and composition operators between two Orlicz spaces" by Yousef Estaremi. Abstract: In this paper we consider composition operator $C_{\varphi} generated by nonsingular measurable transformation $T$ and multiplication operator $M_u$ generated by measurable function $u$ between two different Or- licz spaces, then we investigate boundedness, compactness and essential norm of multiplication and composition operators in term of properties of the mapping $\varphi$, the function $u$ and the measure space $(X, \Sigma, \mu)$. Archive classification: math.FA Submitted from: estaremi(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.4830 or http://arXiv.org/abs/1301.4830

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Abstract of a paper by Antonio J. Guirao and Olena Kozhushkina
by alspach＠math.okstate.edu 30 Jan '13

30 Jan '13

This is an announcement for the paper "The Bishop-Phelps-Bollob\'as property for numerical radius in $\ell_1(\mathbb{C})$" by Antonio J. Guirao and Olena Kozhushkina. Abstract: We show that the set of bounded linear operators from $X$ to $X$ admits a Bishop-Phelps-Bollob\'as type theorem for numerical radius whenever $X$ is $\ell_1(\mathbb{C})$ or $c_0(\mathbb{C})$. As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollob\'as theorem for $\ell_1(\mathbb{C})$. Archive classification: math.FA Mathematics Subject Classification: 46B20, 47A12 Submitted from: okozhush(a)math.kent.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.4574 or http://arXiv.org/abs/1301.4574

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