## Linear Operators: General theory |

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Page 243

some of the concrete spaces defined above satisfy these axioms , and hence are

special cases of abstract

**Hilbert space**has been defined by a set of abstract axioms . It is noteworthy thatsome of the concrete spaces defined above satisfy these axioms , and hence are

special cases of abstract

**Hilbert space**. Thus , for instance , the n - dimensional ...Page 247

closely related , especially in its elementary geometrical aspects , to the

Euclidean or finite dimensional unitary spaces . It is not immediate from the

definition ( 2.26 ) ...

**Hilbert Space**Of the infinite dimensional B - spaces ,**Hilbert space**is the mostclosely related , especially in its elementary geometrical aspects , to the

Euclidean or finite dimensional unitary spaces . It is not immediate from the

definition ( 2.26 ) ...

Page 256

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X1 , ... , Xn

are

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X1 , ... , Xn

are

**Hilbert spaces**then it will always be understood , sometimes without explicit ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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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 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