## Linear Operators: General theory |

### From inside the book

Results 1-3 of 83

Page 54

Since the

Since the

**mapping**x = x / k , is a homeomorphism of X with itself , by 10 ( ii ) , the proof is complete . Q.E.D. We now are in a position to prove a number ...Page 455

In this case , the

In this case , the

**mapping**H : K → lz , defined by H ( k ) = [ gi ( k ) ] , is a continuous**mapping**of K onto a compact convex subset K , of the Hilbert ...Page 525

log \ T 1/4 valued u - measurable functions defined on S. Let T be a linear

log \ T 1/4 valued u - measurable functions defined on S. Let T be a linear

**mapping**of X into M. If T is a bounded linear**mapping**of X into L ( S , E , u ) ...### 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 |

quences | 26 |

Copyright | |

81 other sections not shown

### Other editions - View all

### Common terms and phrases

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