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

Extracta Mathematicae (1991)

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

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## Abstract

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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 &gt; 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | &lt; 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). (...)

## How to cite

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González, 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 &gt; 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | &lt; 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 &gt; 0, ∃M ∈ S∞(X), ∀x ∈ SM, | ||Tx|| - α | &lt; 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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