Sur quelques extensions au cadre banachique de la notion d'opérateur de Hilbert-Schmidt

Said Amana Abdillah; Jean Esterle; Bernhard H. Haak

Studia Mathematica (2015)

  • Volume: 227, Issue: 3, page 193-218
  • ISSN: 0039-3223

Abstract

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In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operator: p-summing operators, γ-summing or γ-radonifying operators, weakly* 1-nuclear operators and classes of operators defined via factorization properties. We introduce the class PS₂(E;F) of pre-Hilbert-Schmidt operators as the class of all operators u: E → F such that w ∘ u ∘ v is Hilbert-Schmidt for every bounded operator v: H₁ → E and every bounded operator w: F → H₂, where H₁ and H₂ are Hilbert spaces. Besides the trivial case where one of the spaces E or F is a ''Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces E or F is a Hilbert space.

How to cite

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Said Amana Abdillah, Jean Esterle, and Bernhard H. Haak. "Sur quelques extensions au cadre banachique de la notion d'opérateur de Hilbert-Schmidt." Studia Mathematica 227.3 (2015): 193-218. <http://eudml.org/doc/285932>.

@article{SaidAmanaAbdillah2015,
author = {Said Amana Abdillah, Jean Esterle, Bernhard H. Haak},
journal = {Studia Mathematica},
keywords = {Hilbert-Schmidt operator; universally factorisable operator; $\mathcal \{L\}_\infty $ factorisable operator; $\mathcal \{L\}_1$ factorisable operator; Hilbert-Schmidt factorisable operator; -summing operator; -radonifying operator; almost summing operator; $\gamma $-summing operator; Rademacher-summing operator; weak*-nuclear operator; pre-Hilbert-Schmidt operator},
language = {fre},
number = {3},
pages = {193-218},
title = {Sur quelques extensions au cadre banachique de la notion d'opérateur de Hilbert-Schmidt},
url = {http://eudml.org/doc/285932},
volume = {227},
year = {2015},
}

TY - JOUR
AU - Said Amana Abdillah
AU - Jean Esterle
AU - Bernhard H. Haak
TI - Sur quelques extensions au cadre banachique de la notion d'opérateur de Hilbert-Schmidt
JO - Studia Mathematica
PY - 2015
VL - 227
IS - 3
SP - 193
EP - 218
LA - fre
KW - Hilbert-Schmidt operator; universally factorisable operator; $\mathcal {L}_\infty $ factorisable operator; $\mathcal {L}_1$ factorisable operator; Hilbert-Schmidt factorisable operator; -summing operator; -radonifying operator; almost summing operator; $\gamma $-summing operator; Rademacher-summing operator; weak*-nuclear operator; pre-Hilbert-Schmidt operator
UR - http://eudml.org/doc/285932
ER -

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