Note on operational quantities and Mil'man isometry spectrum
- Martinón Cejas, Antonio
- González Ortiz, Manuel
ISSN: 0213-8743
Année de publication: 1991
Volumen: 6
Número: 2-3
Pages: 129-131
Type: Article
D'autres publications dans: Extracta mathematicae
Résumé
Let X and Y be infinite dimensional Banach spaces and let L(X,Y) be the class of all (linear continuous) operators acting between X and Y. Mil'man [5] introduced the isometry spectrum I(T) of T Î L(X,Y) in the following way: I(T) = {a = 0: " e > 0, $M Î S8(X), "x Î SM, | ||Tx|| - a | < e}}, where S8(X) is the set of all infinite dimensional closed subspaces of X and SM := {x Î M: ||x|| = 1} is the unit sphere of M Î S8(X). (...)