When every multilinear mapping is multiple summing

DOI10.1002/mana.200710112zbMath1191.46041arXiv0801.3410OpenAlexW1988371623MaRDI QIDQ3643556

Daniel M. Pellegrino, Geraldo Botelho

Publication date: 9 November 2009

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.3410

zbMATH Keywords

multilinear mappingsabsolutely summingmultiple summing

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) (Spaces of) multilinear mappings, polynomials (46G25) Ideals of polynomials and of multilinear mappings in operator theory (47L22)

Related Items (20)

Nonlinear absolutely summing operators revisited ⋮ On coincidence results for summing multilinear operators: interpolation, \(\ell_1\)-spaces and cotype ⋮ On the Bohnenblust-Hille inequality for multilinear forms ⋮ A regularity principle in sequence spaces and applications ⋮ Composition results for strongly summing and dominated multilinear operators ⋮ Summing multilinear operators by blocks: the isotropic and anisotropic cases ⋮ Unified Grothendieck's and Kwapień's theorems for multilinear operators ⋮ Towards sharp Bohnenblust–Hille constants ⋮ Traced tensor norms and multiple summing multilinear operators ⋮ On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility ⋮ Some techniques on nonlinear analysis and applications ⋮ Multilinear extensions of absolutely \((p;q;r)\)-summing operators ⋮ Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches ⋮ Hilbert-Schmidt and multiple summing operators ⋮ Multilinear variants of Maurey and Pietsch theorems and applications ⋮ Complex interpolation and summability properties of multilinear operators ⋮ Coordinatewise multiple summing operators in Banach spaces ⋮ Absolutely summing multilinear operators via interpolation ⋮ Diagonal extendible multilinear operators between \(\ell_p\)-spaces ⋮ Generalized multiple summing multilinear operators on Banach spaces

Cites Work

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• Fully, absolutely summing and Hilbert-Schmidt multilinear mappings
• Multiple summing operators on \(C(K)\) spaces
• Fully summingmultilinear and holomorphicmappings into Hilbert spaces
• A tensor norm preserving unconditionality for $\mathcal{L}_p$-spaces
• Multilinear extensions of Grothendieck's theorem

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