## Linear Operators: General theory |

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Page 37

If T is a

If T is a

**linear operator**on X to X , it is said to be a**linear operator**in X. For such operators the symbol T2 is used for TT , and , inductively , Tn for ...Page 486

The set of compact operators is closed in the uniform operator topology of B ( X ... Linear combinations of compact

The set of compact operators is closed in the uniform operator topology of B ( X ... Linear combinations of compact

**linear operators**are compact operators ...Page 513

... then there exists a bounded

... then there exists a bounded

**linear operator**T : X + Y such that T * = U. 14 Let T be a linear , but not necessarily continuous , mapping between B ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero