## Linear Operators: General theory |

### From inside the book

Results 1-3 of 66

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

9. Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of the product Pxex Y. , where Y. = Y , under the mapping T → PxexTx . Show that the strong topology of

9. Exercises 1 The space B ( X , Y ) is algebraically isomorphic to a subspace of the product Pxex Y. , where Y. = Y , under the mapping T → PxexTx . Show that the strong topology of

**operators**in B ( X , Y ) is identical with the usual ...Page 540

**operator**and the**operator**mapping into a weakly complete space X. Weakly compact**operators**from C [ 0 , 1 ] to X were treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact**operators**with domain C ( S ) was given by ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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