Linear Operators, Part 1 |
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Page 373
This generalizes and abstracts a result proved for closed linear manifolds in L2 [
0 , 1 ] by E. Fischer [ 2 ] . The fact that a linear manifold which is not dense in the
entire space has a non - zero orthogonal complement ( proved in 4.4 ) was ...
This generalizes and abstracts a result proved for closed linear manifolds in L2 [
0 , 1 ] by E. Fischer [ 2 ] . The fact that a linear manifold which is not dense in the
entire space has a non - zero orthogonal complement ( proved in 4.4 ) was ...
Page 385
They are essentially due , at least in the real case , to Stone [ 1 ] , although his
terminology and proofs often differ from that given here . It should be mentioned
that Theorem 6.22 was proved independently by Čech [ 1 ] only slightly later .
They are essentially due , at least in the real case , to Stone [ 1 ] , although his
terminology and proofs often differ from that given here . It should be mentioned
that Theorem 6.22 was proved independently by Čech [ 1 ] only slightly later .
Page 463
124 ] also proved that in the case of a separable space hese notions coincide
with that of closure in the X topology of X * . Alaoglu ( 1 ; p . 256 ] and Kakutani ( 2
; p . 170 ) independently established the equivalence of these types of closure ...
124 ] also proved that in the case of a separable space hese notions coincide
with that of closure in the X topology of X * . Alaoglu ( 1 ; p . 256 ] and Kakutani ( 2
; p . 170 ) independently established the equivalence of these types of closure ...
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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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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 |