Hilbert-Schmidt and multiple summing operators
type: Item
instance of: scholarly article
title: Hilbert-Schmidt and multiple summing operators
zbMATH Open document ID: 1266.47085
author: Gabriela Badea
author: Dumitrŭ Popa
published in: Collectanea Mathematica
publication date: 2012-12-04T00:00:00Z
review text: The main result of the paper is a characterization of multiple \(p\)-summing operators for \(p\geq2\) in the case where the range and some of the factors of the Cartesian product are Hilbert spaces. Some coincidence results for multiple \(p\)-summing operators are obtained as a consequence of the aforementioned characterization. The last section presents a lot of interesting examples of summing operators.
Mathematics Subject Classification ID: 47H60
Mathematics Subject Classification ID: 46B25
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 6112450
zbMATH Keywords: multiple \(p\)-summing operator
zbMATH Keywords: Hilbert-Schmidt operator
zbMATH Keywords: coincidence theorems
reviewed by: Daniel Pellegrino
MaRDI profile type: Publication
full work available at URL: s13348-010-0028-2
OpenAlex ID: W2068401471
cites work: A multilinear Lindenstrauss theorem
cites work: On the absolute convergence of Dirichlet series
cites work: Multilinear extensions of Grothendieck's theorem
cites work: Complex interpolation and summability properties of multilinear operators
cites work: When every multilinear mapping is multiple summing
cites work: On the multilinear generalizations of the concept of absolutely summing operators
cites work: Q4023934
cites work: Bohr's strip for vector valued Dirichlet series
cites work: A tensor norm preserving unconditionality for $\mathcal{L}_p$-spaces
cites work: A new multilinear insight on Littlewood's 4/3-inequality
cites work: Coordinatewise multiple summing operators in Banach spaces
cites work: Q4850055
cites work: Q4257163
cites work: Diagonal mappings between sequence spaces
cites work: Fully, absolutely summing and Hilbert-Schmidt multilinear mappings
cites work: Fully summing mappings between Banach spaces
cites work: Q3711155
cites work: A characterization of Hilbert-Schmidt operators
cites work: Fully summingmultilinear and holomorphicmappings into Hilbert spaces
cites work: Multiple summing operators on Banach spaces.
cites work: The inclusion theorem for multiple summing operators
cites work: Multiple summing operators on \(C(K)\) spaces
cites work: Comparing different classes of absolutely summing multilinear operators
cites work: Q5186213
cites work: Q3715635
cites work: Reverse inclusions for multiple summing operators
cites work: Multilinear variants of Maurey and Pietsch theorems and applications
cites work: Operator ideals and spaces of bilinear operators
DOI: 10.1007/S13348-010-0028-2
description: scientific article; zbMATH DE number 6112450