The inclusion theorem for multiple summing operators

DOI10.4064/sm165-3-5zbMath1064.47057OpenAlexW1970240397MaRDI QIDQ4821295

David Pérez-García

Publication date: 11 October 2004

Published in: Studia Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/sm165-3-5

zbMATH Keywords

Hilbert-Schmidt operatorsmultilinear operatorsabsolutely summing operatorsGrothendieck's theorem\(p\)-summing operators

Mathematics Subject Classification ID

Classical Banach spaces in the general theory (46B25) Inner product spaces and their generalizations, Hilbert spaces (46C99) Multilinear and polynomial operators (47H60)

Related Items (33)

Nonlinear absolutely summing operators revisited ⋮ Multiple summing operators on \(C(K)\) spaces ⋮ Multiple splitting property for dominated bilinear operators ⋮ Direct and reverse inclusions for strongly multiple summing operators ⋮ A regularity principle in sequence spaces and applications ⋮ Ideals of multilinear mappings via Orlicz spaces and translation invariant operators ⋮ A tensor norm preserving unconditionality for $\mathcal{L}_p$-spaces ⋮ Multiple Rademacher means and their applications ⋮ An anisotropic approach to mid summable sequences ⋮ Inclusion theorems for absolutely summing holomorphic mappings ⋮ On multi-ideals and polynomial ideals of Banach spaces: a new approach to coherence and compatibility ⋮ Operators with the Maurey–Pietsch multiple splitting property ⋮ Some techniques on nonlinear analysis and applications ⋮ Coincidence situations for absolutely summing nonlinear mappings ⋮ On summability of nonlinear mappings: a new approach ⋮ Ideals of multilinear forms -- a limit order approach ⋮ 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 ⋮ Multilinear variants of Maurey and Pietsch theorems and applications ⋮ Complex interpolation and summability properties of multilinear operators ⋮ Positive multiple summing and concave multilinear operators on Banach lattices ⋮ Coordinatewise multiple summing operators in Banach spaces ⋮ Inclusions and coincidences for multiple summing multilinear mappings ⋮ Reverse inclusions for multiple summing operators ⋮ Remarks on multiple summing operators on \(C(\Omega)\)-spaces ⋮ Dominated polynomials on infinite dimensional spaces ⋮ Generalized multiple summing multilinear operators on Banach spaces ⋮ A composition theorem for multiple summing operators ⋮ An integral formula for multiple summing norms of operators ⋮ Multiple summability properties for Cohen ‐summing operators

This page was built for publication: The inclusion theorem for multiple summing operators