- Banach - mathdept.okstate.edu

[Banach Space Bulletin Board] Abstract of a paper by E. M. Bednarczuk and K. Lesniewski
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “On weakly sequentially complete Banach spaces” by E. M. Bednarczuk and K. Lesniewski. Abstract: We provide sufficient conditions for a Banach space $Y$ to be weakly sequentially complete. These conditions are expressed in terms of the existence of directional derivatives for cone convex mappings with values in $Y$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04718

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[Banach Space Bulletin Board] Abstract of a paper by Johann Langemets, Vegard Lima and Abraham Rueda Zoca
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Almost square and octahedral norms in tensor products of Banach spaces” by Johann Langemets, Vegard Lima and Abraham Rueda Zoca. Abstract: The aim of this note is to study some geometrical properties like diameter two properties, octahedrality and almost squareness in the setting of (symmetric) tensor product spaces. In particular, we show that the injective tensor product of two octahedral Banach spaces is always octahedral, the injective tensor product of an almost square Banach space with any Banach space is almost square, and the injective symmetric tensor product of an octahedral Banach space is octahedral. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.07090

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[Banach Space Bulletin Board] Abstract of a paper by Angela Capel, Miguel Martin and Javier Meri
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Numerical radius attaining compact linear operators” by Angela Capel, Miguel Martin and Javier Meri. Abstract: We show that there are compact linear operators on Banach spaces which cannot be approximated by numerical radius attaining operators. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.07084

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[Banach Space Bulletin Board] Abstract of a paper by Richard Duong and Friedrich Philipp
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “The effect of perturbations of linear operators on their polar decomposition” by Richard Duong and Friedrich Philipp. Abstract: The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we prove in particular that the partial isometry in the polar decomposition of an operator is stable under perturbations, given that kernel and range of original and perturbed operator satisfy a certain condition. In the matrix case, this condition is weaker than the usually imposed equal-rank condition. It includes the case of semi-Fredholm operators with agreeing nullities and deficiencies, respectively. In addition, we prove a similar perturbation result where the ranges or the kernels of the two operators are assumed to be sufficiently close to each other in the gap metric. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.05304

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[Banach Space Bulletin Board] Abstract of a paper by Dmitrii V. Prokhorov and Vladimir D. Stepanov
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Weighted inequalities for quasilinear integral operators on the semiaxis and application to the Lorentz spaces” by Dmitrii V. Prokhorov and Vladimir D. Stepanov. Abstract: Weighted $L_p-L_r$ inequalities with arbitrary measurable non-negative weights for positive quasilinear integral operators with Oinarov's kernel on the semiaxis are characterized. Application to the boundedness of maximal operator in the Lorentz $\Gamma$−spaces is given. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04884

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[Banach Space Bulletin Board] Abstract of a paper by Bahram Khodsiani and Ali Rejali
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Group Representations on Reflexive Spaces” by Bahram Khodsiani and Ali Rejali. Abstract: For weighted group convoltion measure algebra we construct a representation on reflexsive space. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04638

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[Banach Space Bulletin Board] Abstract of a paper by Nikolaos Roidos
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Closedness and invertibility for the sum of two closed operators” by Nikolaos Roidos. Abstract: We show a Kalton-Weis type theorem for the general case of non-commuting operators. More precisely, we consider sums of two possibly non-commuting linear operators defined in a Banach space such that one of the operators admits bounded $H_{\infty}$-calculus, the resolvent of the other one satisfies some weaker boundedness condition and the commutator of their resolvents has certain decay behavior with respect to the spectral parameters. Under this consideration, we show that the sum is closed and that after a sufficiently large positive shift it becomes invertible, and moreover sectorial. As an application, we employ this result in combination with a resolvent construction technique, and recover a classical result on the existence, uniqueness and maximal $L_p$-regularity of solution for the abstract non-autonomous linear parabolic problem. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04465

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[Banach Space Bulletin Board] Abstract of a paper by Mona Nabiei
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “An effective metric on $C(H,K)$ with normal structure” by Mona Nabiei. Abstract: This study first defines a new metric with normal structure on $C(H,K)$ and then a new technique to prove fixed point theorems for families of non-expansive maps on this metric space. Indeed, it shows that the presence of a bounded orbit implies the existence of a fixed point for a group of h-biholomorphic automorphisms on $C(H,K)$. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.04015

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[Banach Space Bulletin Board] Abstract of a paper by Constantin Costara and Dusan Repov
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “Spectral isometries onto algebras having a separating family of finite-dimensional irreducible representations” by Constantin Costara and Dusan Repov. Abstract: We prove that if $\mathcal{A}$ is a complex, unital semisimple Banach algebra and $\mathcal{B}$ is a complex, unital Banach algebra having a separating family of finite-dimensional irreducible representations, then any unital linear operator from $\mathcal{A}$ onto $\mathcal{B}$ which preserves the spectral radius is a Jordan morphism. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.03964

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[Banach Space Bulletin Board] Abstract of a paper by M. Maia, D. Pellegrino and J. Santos
by Bentuo Zheng (bzheng) 28 Feb '16

28 Feb '16

This is an announcement for the paper “An index of summability for pairs of Banach spaces” by M. Maia, D. Pellegrino and J. Santos. Abstract: We introduce the notion of index of summability for pairs of Banach spaces; for Banach spaces E; F, this index plays the role of a kind of measure of how the m-homogeneous polynomials from E to F are far from being absolutely summing. In some cases the optimal index of summability is computed. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1602.03363

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