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

• Autorzy: Said Amana Abdillah , Jean Esterle , Bernhard H. Haak
• Języki publikacji: FR EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B25: Classical Banach spaces in the general theory
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 3
• Strony: 193-218

Daty

wydano

2015

Twórcy

autor

Said Amana Abdillah

• Université des Comores, Rue de la Corniche, B.P. 2585 Moroni (Comores)

autor

Jean Esterle

• Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence Cedex, France

autor

Bernhard H. Haak

• Institut de Mathématiques de Bordeaux, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence Cedex, France

Identyfikatory

DOI

10.4064/sm227-3-1