# Note on operational quantities and Mil'man isometry spectrum.

Manuel González; Antonio Martinón

Extracta Mathematicae (1991)

- Volume: 6, Issue: 2-3, page 129-131
- ISSN: 0213-8743

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topGonzález, Manuel, and Martinón, Antonio. "Note on operational quantities and Mil'man isometry spectrum.." Extracta Mathematicae 6.2-3 (1991): 129-131. <http://eudml.org/doc/39933>.

@article{González1991,

abstract = {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). (...)},

author = {González, Manuel, Martinón, Antonio},

journal = {Extracta Mathematicae},

keywords = {Espacios normados; Espacios de Banach; Operadores de Fredholm; Operadores singulares; Mil'man isometry spectrum; Tsirelson-like examples of Banach spaces; upper semi-Fredholm operators},

language = {eng},

number = {2-3},

pages = {129-131},

title = {Note on operational quantities and Mil'man isometry spectrum.},

url = {http://eudml.org/doc/39933},

volume = {6},

year = {1991},

}

TY - JOUR

AU - González, Manuel

AU - Martinón, Antonio

TI - Note on operational quantities and Mil'man isometry spectrum.

JO - Extracta Mathematicae

PY - 1991

VL - 6

IS - 2-3

SP - 129

EP - 131

AB - 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). (...)

LA - eng

KW - Espacios normados; Espacios de Banach; Operadores de Fredholm; Operadores singulares; Mil'man isometry spectrum; Tsirelson-like examples of Banach spaces; upper semi-Fredholm operators

UR - http://eudml.org/doc/39933

ER -

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