Linear Operators, Part 1 |
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Page 245
An n - dimensional B - space is equivalent to En . 4 COROLLARY . Every linear
operator on a finite dimensional normed linear space is continuous . Proof . Let {
b1 , ... , bn } be a Hamel basis for the finite dimensional normed linear space X so
...
An n - dimensional B - space is equivalent to En . 4 COROLLARY . Every linear
operator on a finite dimensional normed linear space is continuous . Proof . Let {
b1 , ... , bn } be a Hamel basis for the finite dimensional normed linear space X so
...
Page 246
Then the dimension of X ** is finite , and , since X is equivalent to a subspace of X
** ( II.3.19 ) , the dimension of X is finite . ... preliminary discussion in Section IV.
11 ) of infinite dimensional F - spaces with zero dimensional conjugate spaces .
Then the dimension of X ** is finite , and , since X is equivalent to a subspace of X
** ( II.3.19 ) , the dimension of X is finite . ... preliminary discussion in Section IV.
11 ) of infinite dimensional F - spaces with zero dimensional conjugate spaces .
Page 556
Spectral Theory in a Finite Dimensional Space Throughout this section , X will
denote a finite dimensional complex B - space , and T a linear operator in B ( X ) .
Our aim is to study the algebraic and topological properties of T. This is achieved
...
Spectral Theory in a Finite Dimensional Space Throughout this section , X will
denote a finite dimensional complex B - space , and T a linear operator in B ( X ) .
Our aim is to study the algebraic and topological properties of T. This is achieved
...
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Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
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Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero
Bibliographic information
| Title | Linear Operators, Part 1 Linear Operators, Jacob T. Schwartz Volume 7 of Mathematics, Pure, Applied Volume 7 of Pure and applied mathematics, ISSN 0079-8185 Volume 7 of Pure and applied mathematics. A series of texts and monographs |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of California |
| Digitized | 26 Jun 2018 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |