## Linear Operators: General theory |

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Page 72

I.11 ) is a

I.11 ) is a

**B**-**space**( or an F -**space**with the metric \ x + 3 ) = inf ( x + z . n ( Hint : Given a Cauchy sequence in X / 3 , define a subsequence for which XxXx + 1 + 31 < 2 - k , k = 1 , 2 , ... , and show that a Cauch sequence in X ...Page 89

In the definitions of F- and

In the definitions of F- and

**B**-**spaces**, we required the**spaces**to be complete in their metric topology . Occasionally it is necessary to consider ... Let X be a linear**space**satisfying properties ( i ) and ( ii ) of Definition 1.10 .Page 238

A List of Special

A List of Special

**Spaces**We give below a list of various special**B**- and F-**spaces**. With the one exception of Hilbert**space**, each of them will consist of real or complex valued functions /, g defined on a specified domain S. Here, ...### 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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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