## 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 494

It is clear that the operator T , defined by ( b ) , is a bounded

It is clear that the operator T , defined by ( b ) , is a bounded

**linear operator**on C ( S ) to X whose adjoint T * is given by ( d ) .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero