Resumen de Note on operational quantities and Mil'man isometry spectrum

Antonio Martinón Cejas, Manuel González Ortiz

• 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). (...)