## Linear Operators: General theory |

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Page 584

... and an operator U such that fn ( T ) → U and U2 = T. 32 Let In € F ( T ) , and suppose that fn ( T ) converges in the

... and an operator U such that fn ( T ) → U and U2 = T. 32 Let In € F ( T ) , and suppose that fn ( T ) converges in the

**uniform**topology of operators .Page 594

Thus f ( T ) h ( T ) = E ( 01 ) , so that In ( T ) E ( 01 ) converges in the

Thus f ( T ) h ( T ) = E ( 01 ) , so that In ( T ) E ( 01 ) converges in the

**uniform**topology of operators . It follows from [ * ] that { fn ( T ) ...Page 857

remarks on , ( 730 )

remarks on , ( 730 )

**Uniform**operator topology , definition , VI.1.1 ( 475 ) properties , V1.9.11-12 ( 512-513 ) Unit , of a group , ( 34 ) Unit sphere in a ...### 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