## Linear Operators: General theory |

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Page 188

The best known example of Theorem 2 and its

The best known example of Theorem 2 and its

**Corollary**6 is obtained by taking ( S , E , a ) to be the Borel - Lebesgue measure on the real line for i = 1 , ... , n . Then S = P , S , is n - dimensional Euclidean space , and u = My X ..Page 246

The following

The following

**corollary**was established during the first part of the preceding proof . 7**COROLLARY**. If { b1 , ... , bn } is a Hamel basis for the normed linear space X then the functionals b * , i = 1 ...Page 422

let pe + 11

let pe + 11

**COROLLARY**. Let f be a linear functional on the linear space X , and let I be a total subspace of x * . Then the following statements are equivalent : ( i ) f is in l ' ; ( ii ) | is I - continuous ; ( iii ) Hy { x \ | ( x ) ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isometric isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero