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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 ...
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 ...
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 ...
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 ...
Page 608
In the case of a bounded or unbounded normal operator in a Hilbert space , many of the results of this section become simpler and can be proved more directly by other methods . With these hypotheses considerable extension is possible .
In the case of a bounded or unbounded normal operator in a Hilbert space , many of the results of this section become simpler and can be proved more directly by other methods . With these hypotheses considerable extension is possible .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero