Coordinatewise multiple summing operators in Banach spaces

DOI10.1016/j.jfa.2010.01.008zbMath1205.46026OpenAlexW2081054398MaRDI QIDQ982496

Ursula Schwarting, Dumitru Popa, Andreas Defant

Publication date: 7 July 2010

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2010.01.008

zbMATH Keywords

polynomialsDirichlet seriesBohnenblust-Hille inequalitymultilinear mapsmultiple summing operatorsLittlewood's \(4/3\) theorem

Mathematics Subject Classification ID

(Spaces of) multilinear mappings, polynomials (46G25) Ideals of polynomials and of multilinear mappings in operator theory (47L22)

Related Items (51)

Summability of the coefficients of a multilinear form ⋮ Nonlinear absolutely summing operators revisited ⋮ Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators ⋮ On almost summing polynomials and multilinear mappings ⋮ Estimates for the asymptotic behaviour of the constants in the Bohnenblust–Hille inequality ⋮ Absolutely summing multilinear operators on \(\ell_p\) spaces ⋮ Blei's inequality and coordinatewise multiple summing operators ⋮ On the constants of the Bohnenblust-Hille and Hardy-Littlewood inequalities ⋮ Direct and reverse inclusions for strongly multiple summing operators ⋮ On coincidence results for summing multilinear operators: interpolation, \(\ell_1\)-spaces and cotype ⋮ A permanence property for dominated multilinear operators ⋮ Nuclear multilinear operators with respect to a partition ⋮ Nuclear and multiple 1-summing operators on \(X_1 \times \cdots \times X_k \times c_0\) ⋮ The Bohr radius of the \(n\)-dimensional polydisk is equivalent to \(\sqrt{(\log n) / n}\) ⋮ Ideals of multilinear mappings via Orlicz spaces and translation invariant operators ⋮ Composition results for strongly summing and dominated multilinear operators ⋮ Summing multilinear operators by blocks: the isotropic and anisotropic cases ⋮ Estimates for vector valued Dirichlet polynomials ⋮ Improving the closed formula for subpolynomial constants in the multilinear Bohnenblust-Hille inequalities ⋮ Unified Grothendieck's and Kwapień's theorems for multilinear operators ⋮ Mixing multilinear operators with or without a linear analogue ⋮ The asymptotic growth of the constants in the Bohnenblust-Hille inequality is optimal ⋮ New upper bounds for the constants in the Bohnenblust-Hille inequality ⋮ Multiple Rademacher means and their applications ⋮ Characterizations of new Cohen summing bilinear operators ⋮ Techniques to generate hyper-ideals of multilinear operators ⋮ On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility ⋮ Operators with the Maurey–Pietsch multiple splitting property ⋮ The Bohnenblust-Hille cycle of ideas from a modern point of view ⋮ On summability of nonlinear mappings: a new approach ⋮ Hyper-ideals of multilinear operators ⋮ Lower bounds for the constants in the Bohnenblust–Hille inequality: The case of real scalars ⋮ A subexponential vector-valued Bohnenblust-Hille type inequality ⋮ Swartz type results for nuclear and multiple 1-summing bilinear operators on \(c_0(\mathcal {X})\times c_0(\mathcal {Y})\) ⋮ Bourgain discretization using Lebesgue-Bochner spaces ⋮ Optimal Hardy-Littlewood type inequalities for \(m\)-linear forms on \(\ell_{p}\) spaces with \({1\leq p\leq m}\) ⋮ Multiple summing maps: coordinatewise summability, inclusion theorems and \(p\)-Sidon sets ⋮ Hilbert-Schmidt and multiple summing operators ⋮ Multiple summing, dominated and summing operators on a product of \(l_1\) spaces ⋮ Factorization of absolutely continuous polynomials ⋮ A new distinguishing feature for summing, versus dominated and multiple summing operators ⋮ Bohr's strips for Dirichlet series in Banach spaces ⋮ Bohr radii of vector valued holomorphic functions ⋮ Absolutely summing multilinear operators via interpolation ⋮ Hardy spaces of general Dirichlet series — a survey ⋮ Remarks on multiple summing operators on \(C(\Omega)\)-spaces ⋮ Vector-valued general Dirichlet series ⋮ The inclusion problem for mixed norm spaces ⋮ Generalized multiple summing multilinear operators on Banach spaces ⋮ Multiple summability properties for Cohen ‐summing operators ⋮ Some applications of hypercontractive inequalities in quantum information theory

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