## Linear Operators: General theory |

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Page 243

**Hilbert space**has been defined by a set of abstract axioms . It is noteworthy that some of the concrete spaces defined above satisfy these axioms ...Page 247

**Hilbert Space**Of the infinite dimensional B - spaces ,**Hilbert space**is the most closely related , especially in its elementary geometrical aspects , to the ...Page 256

If , however , each of the spaces X1 , ... , Xn are

If , however , each of the spaces X1 , ... , Xn are

**Hilbert spaces**then it ... that X is the uniquely determined**Hilbert space**with scalar product n ( iv ) ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero