October 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 Alexander Koldobsky
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Slicing inequalities for subspaces of $L_p.$" by Alexander Koldobsky. Abstract: We show that the hyperplane conjecture holds for the classes of $k$-intersection bodies with arbitrary measures in place of volume. Archive classification: math.MG math.FA Mathematics Subject Classification: 52A20 Submitted from: koldobskiya(a)missouri.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.8102 or http://arXiv.org/abs/1310.8102

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Abstract of a paper by Mubariz Garayev
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Solution of invariant subspace problem in the Hilbert space" by Mubariz Garayev. Abstract: By applying methods of Duhamel algebra and reproducing kernels, we prove that every linear bounded operator on the Hardy-Hilbert space H^{2}(D) has a nontrivial invariant subspace. This solves affirmatively the Invariant Subspace Problem in the Hilbert space. Archive classification: math.FA Mathematics Subject Classification: 47A12 Submitted from: mgarayev(a)ksu.edu.sa The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.8055 or http://arXiv.org/abs/1310.8055

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Abstract of a paper by Denny H. Leung
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Ideals of operators on $(\oplus \ell^\infty(n))_{\ell^1}$" by Denny H. Leung. Abstract: The unique maximal ideal in the Banach algebra $L(E)$, $E = (\oplus \ell^\infty(n))_{\ell^1}$, is identified. The proof relies on techniques developed by Laustsen, Loy and Read and a dichotomy result for operators mapping into $L^1$ due to Laustsen, Odell, Schlumprecht and Zs\'{a}k. Archive classification: math.FA Mathematics Subject Classification: 46L10, 46H10 Submitted from: matlhh(a)nus.edu.sg The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.7352 or http://arXiv.org/abs/1310.7352

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Abstract of a paper by Denny H. Leung and Lei Li
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Order isomorphisms on function spaces" by Denny H. Leung and Lei Li. Abstract: The classical theorems of Banach and Stone, Gelfand and Kolmogorov, and Kaplansky show that a compact Hausdorff space $X$ is uniquely determined by the linear isometric structure, the algebraic structure, and the lattice structure, respectively, of the space $C(X)$. In this paper, it is shown that for rather general subspaces $A(X)$ and $A(Y)$ of $C(X)$ and $C(Y)$ respectively, any linear bijection $T: A(X) \to A(Y)$ such that $f \geq 0$ if and only if $Tf \geq 0$ gives rise to a homeomorphism $h: X \to Y$ with which $T$ can be represented as a weighted composition operator. The three classical results mentioned above can be derived as corollaries. Generalizations to noncompact spaces and other function spaces such as spaces of uniformly continuous functions, Lipschitz functions and differentiable functions are presented. Archive classification: math.FA Mathematics Subject Classification: 46E15 Submitted from: matlhh(a)nus.edu.sg The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.7351 or http://arXiv.org/abs/1310.7351

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Abstract of a paper by Andrei Dorogovtsev and Mikhail Popov
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Basis entropy in Banach spaces" by Andrei Dorogovtsev and Mikhail Popov. Abstract: We introduce and study two notions of entropy in a Banach space X with a normalized Schauder basis . The geometric entropy E(A) of a subset A of X is defined to be the infimum of radii of compact bricks containing A. We obtain several compactness characterizations for bricks (Theorem 3.7) useful for main results. We also obtain sufficient conditions on a set in a Hilbert space to have finite unconditional entropy. For Banach spaces without a Schauder basis we offer another entropy, called the Auerbach entropy. Finally, we pose some open problems. Archive classification: math.FA Mathematics Subject Classification: 46B50, 46B15, 60H07 Remarks: 22 pages Submitted from: adoro(a)imath.kiev.ua The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.7248 or http://arXiv.org/abs/1310.7248

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Abstract of a paper by M A Sofi
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Around finite-dimensionality in functional analysis" by M A Sofi. Abstract: As objects of study in functional analysis, Hilbert spaces stand out as special objects of study as do nuclear spaces in view of a rich geometrical structure they possess as Banach and Frechet spaces, respectively. On the other hand, there is the class of Banach spaces including certain function spaces and sequence spaces which are distinguished by a poor geometrical structure and are subsumed under the class of so-called Hilbert-Schmidt spaces. It turns out that these three classes of spaces are mutually disjoint in the sense that they intersect precisely in finite dimensional spaces. However, it is remarkable that despite this mutually exclusive character, there is an underlying commonality of approach to these disparate classes of objects in that they crop up in certain situations involving a single phenomenon-the phenomenon of finite dimensionality-which, by definition, is a generic term for those properties of Banach spaces which hold good in finite dimensional spaces but fail in infinite dimension. Archive classification: math.FA Mathematics Subject Classification: 46A11, 46C15 Citation: RACSAM 2013 Remarks: 22 pages Submitted from: aminsofi(a)kashmiruniversity.ac.in The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.7165 or http://arXiv.org/abs/1310.7165

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Abstract of a paper by S. J. Dilworth and B. Randrianantoanina
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Almost transitive and maximal norms in Banach spaces" by S. J. Dilworth and B. Randrianantoanina. Abstract: We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This answers a problem posed by Deville, Godefroy and Zizler in 1993. We obtain this as a consequence of a new property of almost transitive spaces with a Schauder basis, namely we prove that in such spaces the unit vector basis of $\ell_2^2$ belongs to the two-dimensional asymptotic structure and we obtain some information about the asymptotic structure in higher dimensions. We also obtain several other results about properties of classical, Tsirelson type and non-commutative Banach spaces with almost transitive norms. Further, we prove that the spaces $\ell_p$, $1<p<\infty$, $p\ne 2$, have continuum different renormings with 1-unconditional bases each with a different maximal isometry group, and that every symmetric space other than $\ell_2$ has at least a countable number of such renormings. On the other hand we show that the spaces $\ell_p$, $1<p<\infty$, $p\ne 2$, have continuum different renormings each with an isometry group which is not contained in any maximal bounded subgroup of the group of isomorphisms of $\ell_p$. This answers a question of Wood. Archive classification: math.FA Mathematics Subject Classification: 46B04, 46B03, 22F50 Submitted from: randrib(a)miamioh.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.7139 or http://arXiv.org/abs/1310.7139

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Abstract of a paper by Eve Oja
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "Principle of local reflexivity respecting subspaces" by Eve Oja. Abstract: We obtain a strengthening of the principle of local reflexivity in a general form. The added strength makes local reflexivity operators respect given subspaces. Applications are given to bounded approximation properties of pairs, consisting of a Banach space and its subspace. Archive classification: math.FA Submitted from: eve.oja(a)ut.ee The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.6232 or http://arXiv.org/abs/1310.6232

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Abstract of a paper by Bunyamin Sari and Konstantinos Tyros
by alspach＠math.okstate.edu 31 Oct '13

31 Oct '13

This is an announcement for the paper "On the structure of the set of the higher order spreading models" by Bunyamin Sari and Konstantinos Tyros. Abstract: We generalize some results concerning the classical notion of a spreading model for the spreading models of order $\xi$. Among them, we prove that the set $SM_\xi^w(X)$ of the $\xi$-order spreading models of a Banach space $X$ generated by subordinated weakly null $\mathcal{F}$-sequences endowed with the pre-partial order of domination is a semi-lattice. Moreover, if $SM_\xi^w(X)$ contains an increasing sequence of length $\omega$ then it contains an increasing sequence of length $\omega_1$. Finally, if $SM_\xi^w(X)$ is uncountable, then it contains an antichain of size the continuum. Archive classification: math.FA Mathematics Subject Classification: 46B06, 46B25, 46B45 Remarks: 23 pages Submitted from: chcost(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1310.5429 or http://arXiv.org/abs/1310.5429

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