## Linear Operators: General theory |

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Page 37

and if T ( x + y ) = Tx + Ty , Tax ) Tx + Ty , Tax ) = aTx for every a € 0 and every pair x , y of vectors in the domain of T. Thus a

and if T ( x + y ) = Tx + Ty , Tax ) Tx + Ty , Tax ) = aTx for every a € 0 and every pair x , y of vectors in the domain of T. Thus a

**linear transformation**on a linear space X is a homomorphism on the additive group & which commutes ...Page 486

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

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

**linear operators**are compact operators , and any product of a compact**linear operator**and a bounded linear ...Page 513

13 If U : Y * → X * is a linear mapping which is continuous with the y topology in Y * and the X topology in X * , then there exists a bounded

13 If U : Y * → X * is a linear mapping which is continuous with the y topology in Y * and the X topology in X * , then there exists a bounded

**linear operator**T : X → Y such that T * = U. 14 Let T be a linear , but not necessarily ...### 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 | |

91 other sections not shown

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