## Linear Operators: General theory |

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Page 37

and if T ( x + y ) = 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 ) = 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 X which commutes with the operations ...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 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 ) . From IV.10.2 we conclude that T * maps the unit sphere of X * into a conditionally weakly compact ...### 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 continuous functions 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 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