## Linear Operators: General theory |

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Page 373

This generalizes and abstracts a result

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

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

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 .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains 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 Hilbert space 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