Some continuity properties of linear transformations in normed spaces
Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 243-247
Voir la notice de l'article provenant de la source Cambridge University Press
Let X and Y be normed spaces and let L(X, Y) denote the set of linear transformations (henceforth called “operators”) T with domain a linear subspace D(T) of X and range R(T) contained in Y. The restriction of T to a subspace E is denoted by T/E; by the usual convention T|E = T|E∩ D(T). For a given linear subspace E the family of infinite dimensional ssubspaces of E is denoted by (E). An operator Tis said to have a certain property P ubiquitously if every E ∈ (X) contains an F ∈(E) for which T|F has property P For example, T is ubiquitously continuous if each E ∈(X) contains an F∈ (E) for which T|F is continuous. In the present note we shall characterize ubiquitous continuity, isomorphy, precompactness and smallness. A subspace of X is called a principal subspace if it is closed and of finite codimension in X. The restriction of an operator to a principal subspace will be called a principal restriction. The symbol T will always denote an arbitrary operator in L(X, Y).
Cross, R. W. Some continuity properties of linear transformations in normed spaces. Glasgow mathematical journal, Tome 30 (1988) no. 2, pp. 243-247. doi: 10.1017/S0017089500007291
@article{10_1017_S0017089500007291,
author = {Cross, R. W.},
title = {Some continuity properties of linear transformations in normed spaces},
journal = {Glasgow mathematical journal},
pages = {243--247},
year = {1988},
volume = {30},
number = {2},
doi = {10.1017/S0017089500007291},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007291/}
}
TY - JOUR AU - Cross, R. W. TI - Some continuity properties of linear transformations in normed spaces JO - Glasgow mathematical journal PY - 1988 SP - 243 EP - 247 VL - 30 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500007291/ DO - 10.1017/S0017089500007291 ID - 10_1017_S0017089500007291 ER -
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