February 2017 - Banach - mathdept.okstate.edu

April 7-9, 2017 - Informal Analysis Seminar at Kent State
by Artem Zvavitch 07 Feb '17

07 Feb '17

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, April 7 - 9, 2017. This time, the theme of this meeting will be differentiation in finite and infinite dimensional spaces. The seminar will feature talks by Daniel Azagra (Universidad Complutense de Madrid), Estibalitz Durand-Cartagena (Universidad Complutense de Madrid), Piotr Hajlasz (University of Pittsburgh), Jesús Jaramillo (Universidad Complutense de Madrid), Manuel Maestre (University of Valenci), Vladimir Peller (Michigan State University), Patrick J. Rabier (University of Pittsburgh), Pilar Rueda (Universidad de Valencia), Nageswari Shanmugalingam (University of Cincinnati). Similar to previous years, the plan of the meeting will be to have two expository, introductory talks on Friday afternoon, April 7, which definitely will be accessible to graduate students. The meeting will end by lunchtime on Sunday, April 9. This time the seminar is supported by Elsevier and Kent State University. Funding is available to cover the local (and possibly 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/~zvavitch/informal/Informal_Analysis_Seminar/April… We encourage you to register as soon as possible, but to receive support and/or help with hotel reservation, please register before March 6st, 2017. 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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Abstract of a paper by A.K.Motovilov, A.A.Shkalikov
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Unconditional bases of subspaces related to non-self-adjoint perturbations of self-adjoint operators” by A.K.Motovilov<https://arxiv.org/find/math/1/au:+Motovilov_A/0/1/0/all/0/1>, A.A.Shkalikov<https://arxiv.org/find/math/1/au:+Shkalikov_A/0/1/0/all/0/1>. Abstract: Assume that $T$ is a self-adjoint operator on a Hilbert space $\mathcal{H}$ and that the spectrum of $T$ is confined in the union $\cup_{j\inJ}\Delta_j, J\subset\mathbb{Z}$, of segments $\Delta_j=[\alpha_j,\beta_j]\subset\mathbb{R}$ such that $\alpha_{j+1}>\beta_j$ and $$\inf_j(\alpha_{j+1}-beta_j)=d>0$$. If $B$ is a bounded (in general non-self-adjoint) perturbation of $T$ with $\|B\|=:b<d/2$ then the spectrum of the perturbed operator $A=T+B$ lies in the union $\cup_{j\inJ} U_b(\Delta_j)$ of the mutually disjoint closed $b$-neighborhoods $U_b(\Delta_j)$ of the segments $\Delta_j$ in $\mathbb{C}$. Let $Q_j$ be the Riesz projection onto the invariant subspace of $A$ corresponding to the part of the spectrum of $A$ lying in $U_b(\Delta_j)$. Our main result is as follows: The subspaces $\mathcalL}_j=Q_j(\mathcal{H}), j\in J$, form an unconditional basis in the whole space $\mathcal{H}$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.06296

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Abstract of a paper by Nicolas Monod
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Fixed points in convex cones” by Nicolas Monod<https://arxiv.org/find/math/1/au:+Monod_N/0/1/0/all/0/1>. Abstract: We propose a fixed-point property for group actions on cones in topological vector spaces. In the special case of equicontinuous actions, we prove that this property always holds; this statement extends the classical Ryll-Nardzewski theorem for Banach spaces. When restricting to cones that are locally compact in the weak topology, we prove that the property holds for all distal actions, thus extending the general Ryll-Nardzewski theorem for all locally convex spaces. Returning to arbitrary actions, the proposed fixed-point property becomes a group property, considerably stronger than amenability. Equivalent formulations are established and a number of closure properties are proved for the class of groups with the fixed-point property for cones. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.05537

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Abstract of a paper by Willian Hans Goes Corrêa
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Type, cotype and twisted sums induced by complex interpolation” by Willian Hans Goes Corrêa<https://arxiv.org/find/math/1/au:+Correa_W/0/1/0/all/0/1>. Abstract: This paper deals with extensions or twisted sums of Banach spaces that come induced by complex interpolation and the relation between the type and cotype of the spaces in the interpolation scale and the nontriviality and singularity of the induced extension. The results are presented in the context of interpolation of families of Banach spaces, and are applied to the study of submodules of Schatten classes. We also obtain nontrivial extensions of spaces without the CAP which also fail the CAP. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.07084

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Abstract of a paper by Ryan M. Causey
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “The Szlenk index of $L_p(X)$ and $A_p$” by Ryan M. Causey<https://arxiv.org/find/math/1/au:+Causey_R/0/1/0/all/0/1>. Abstract: Given a Banach space $X$, a $w^*$-compact subset of $X^*$, and $1<p<\infty$, we provide an optimal relationship between the Szlenk index of $K$ and the Szlenk index of an associated subset of $L_p(X)^*$. As an application, given a Banach space X, we prove an optimal estimate of the Szlenk index of $L_p(X)$ in terms of the Szlenk index of $X$. This extends a result of H\'ajek and Schlumprecht to uncountable ordinals. More generally, given an operator $A: X\rightarrow Y$, we provide an estimate of the Szlenk index of the "pointwise $A$" operator $A_p: L_p(X)\rightarrow L_p(Y)$ in terms of the Szlenk index of $A$. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.06226

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Abstract of a paper by Trond A. Abrahamsen, Vegard Lima
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Relatively weakly open convex combinations of slices” by Trond A. Abrahamsen<https://arxiv.org/find/math/1/au:+Abrahamsen_T/0/1/0/all/0/1>, Vegard Lima<https://arxiv.org/find/math/1/au:+Lima_V/0/1/0/all/0/1>. Abstract: We show that $c_0$, and in fact $C(K)$ for any scattered compact Hausdorff space $K$, have the property that finite convex combinations of slices of the unit ball are relatively weakly open. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.06169

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Abstract of a paper by Loic Gaillard, Pascal Lefèvre
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Lacunary Müntz spaces: isomorphisms and Carleson embeddings” by Loic Gaillard<https://arxiv.org/find/math/1/au:+Gaillard_L/0/1/0/all/0/1>, Pascal Lefèvre<https://arxiv.org/find/math/1/au:+Lefevre_P/0/1/0/all/0/1>. Abstract: In this paper we prove that $M_{\Lambda}^p$ is almost isometric to $\ell_p$ in the canonical way when $\Lambda$ is lacunary with a large ratio. On the other hand, our approach can be used to study also the Carleson measures for M\"untz spaces $M_{\Lambda}^p$ when $\Lambda$ is lacunary. We give some necessary and some sufficient conditions to ensure that a Carleson embedding is bounded or compact. In the hilbertian case, the membership to Schatten classes is also studied. When $\Lambda$ behaves like a geometric sequence the results are sharp, and we get some characterizations. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.05807

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Abstract of a paper by Artsrun Sargsyan, Martin Grigoryan
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Universal function for a weighted space $L^1_u[0,1]$” by Artsrun Sargsyan<https://arxiv.org/find/math/1/au:+Sargsyan_A/0/1/0/all/0/1>, Martin Grigoryan<https://arxiv.org/find/math/1/au:+Grigoryan_M/0/1/0/all/0/1>. Abstract: It is shown that there exist such a function g from $L^1[0,1]$ and a weight function $0<u(x)<=1$ that g is universal for the weighted space $L^1_u[0,1]$ with respect to signs of its Fourier-Walsh coefficients. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.05776

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Abstract of a paper by Razvan Anisca, Valentin Ferenczi, Yolanda Moreno
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “On the classification of positions and of complex structures in Banach spaces” by Razvan Anisca<https://arxiv.org/find/math/1/au:+Anisca_R/0/1/0/all/0/1>, Valentin Ferenczi<https://arxiv.org/find/math/1/au:+Ferenczi_V/0/1/0/all/0/1>, Yolanda Moreno<https://arxiv.org/find/math/1/au:+Moreno_Y/0/1/0/all/0/1>. Abstract: A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or "position") of a Banach space into another and of the relation of isomorphism of complex structures on a real Banach space. The following results are obtained: a) if $X$ is not uniformly finitely extensible, then there exists a space $Y$ for which the relation of position of $Y$ inside $X$ reduces the relation $E_0$ and therefore is not smooth; b) the relation of position of $\ell_p$ inside $\ell_p$, or inside $L_p$, $p\neq 2$, reduces the relation $E_1$ and therefore is not reducible to an orbit relation induced by the action of a Polish group; c) the relation of position of a space inside another can attain the maximum complexity $E_{max}$; d) there exists a subspace of $L_p$, $1\leq p<2$, on which isomorphism between complex structures reduces $E_1$ and therefore is not reducible to an orbit relation induced by the action of a Polish group. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.04263

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Abstract of a paper by Jens Flemming, Daniel Gerth
by Bentuo Zheng (bzheng) 31 Jan '17

31 Jan '17

This is an announcement for the paper “Injectivity and weak$^*$-to-weak continuity suffice for convergence rates in $\ell_1$-regularization” by Jens Flemming<https://arxiv.org/find/math/1/au:+Flemming_J/0/1/0/all/0/1>, Daniel Gerth<https://arxiv.org/find/math/1/au:+Gerth_D/0/1/0/all/0/1>. Abstract: We show that the convergence rate of $\ell_1$-regularization for linear ill-posed equations is always $O(\delta)$ if the exact solution is sparse and if the considered operator is injective and weak$^*$-to-weak continuous. Under the same assumptions convergence rates in case of non-sparse solutions are proven. The results base on the fact that certain source-type conditions used in the literature for proving convergence rates are automatically satisfied. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1701.03460

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