## Linear Operators: General theory |

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Page 477

strong , and the weak

strong , and the weak

**operator**topologies in B ( X , Y ) . It is evident that the uniform**operator**topology is stronger than the strong**operator**topology , and that the strong**operator**topology is stronger than the weak**operator**...Page 494

It is clear that the

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 ...Page 511

Exercises xe X 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of the product Prex Yz , where Ya = Y , under the mapping T → P Tx . Show that the strong topology of

Exercises xe X 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of the product Prex Yz , where Ya = Y , under the mapping T → P Tx . Show that the strong topology of

**operators**in B ( X , Y ) is identical with ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad 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 meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero