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 ∈ L(X,Y) in the following way:
I(T) = {α ≥ 0: ∀ ε > 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | < ε}},
where S∞(X) is the set of all infinite dimensional closed subspaces of X and SM := {x ∈ M: ||x|| = 1} is the unit sphere of M ∈ S∞(X). (...)
@article{urn:eudml:doc:39933,
title = {Note on operational quantities and Mil'man isometry spectrum.},
journal = {Extracta Mathematicae},
volume = {6},
year = {1991},
pages = {129-131},
mrnumber = {MR1185358},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39933}
}
González, Manuel; Martinón, Antonio. Note on operational quantities and Mil'man isometry spectrum.. Extracta Mathematicae, Tome 6 (1991) pp. 129-131. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39933/