## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 70

Page 494

It is clear that the

S ) to X whose adjoint T * is given by ( d ) . From IV . 10 . 2 we conclude that 7 *

maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) ...

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 7 *

maps the unit sphere of X * into a conditionally weakly compact set of rca ( S ) ...

Page 511

Show that the strong topology of

product topology where the strong ... 2 A set AC B ( X , Y ) is compact in the weak

...

Show that the strong topology of

**operators**in B ( X , Y ) is identical with the usualproduct topology where the strong ... 2 A set AC B ( X , Y ) is compact in the weak

**operator**topology if and only if it is closed in the weak**operator**topology and the...

Page 540

Nelson Dunford, Jacob T. Schwartz.

weakly complete space X . Weakly compact

treated by Sirvint [ 3 ] . A very incisive discussion of weakly compact

with ...

Nelson Dunford, Jacob T. Schwartz.

**operator**and the**operator**mapping into aweakly complete space X . Weakly compact

**operators**from C [ 0 , 1 ] to % weretreated by Sirvint [ 3 ] . A very incisive discussion of weakly compact

**operators**with ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

Akad 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 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 transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero