## Linear Operators: General theory |

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Page 54

Since the

Since the

**mapping**x + x | k , is a homeomorphism of X with itself , by 10 ( ii ) , the proof is complete . Q.E.D. We now are in a position to prove a number of basic results about F - spaces . 14 THEOREM . A linear**mapping**of one F ...Page 493

Conversely , if ( a ) and ( b ) are satisfied for the

Conversely , if ( a ) and ( b ) are satisfied for the

**mapping**which sends æ * into u ( * ) # * , then it follows that for each fixed f € C ( S ) the**mapping**→ Ist ( s ) u ( ds ) z * is continuous in the X topology of X * and therefore ...Page 513

12 If H is a Hilbert space , the

12 If H is a Hilbert space , the

**mapping**T → T * of B ( H ) into itself is continuous with either the uniform or weak operator topology . By considering the sequence { Am } defined in Exercise 11 , show that this**mapping**is not ...### 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