## Linear Operators: General theory |

### From inside the book

Results 1-3 of 72

Page 2

... proper subset of the set B if A C B and A + B. The notation ACB , or B Ɔ A , will

is the set whose elements are in B but not in A , i.e. , the set { w \ x e B , æ ¢ A } .

... proper subset of the set B if A C B and A + B. The notation ACB , or B Ɔ A , will

**mean**that A is a proper subset of B. The complement of a set A relative to a set Bis the set whose elements are in B but not in A , i.e. , the set { w \ x e B , æ ¢ A } .

Page 261

The space rba ( S ) is partially ordered by defining u 21 to

) for every E in the field determined by the closed sets . Similarly , the space C ( S

) is partially ordered by defining 1 g to

The space rba ( S ) is partially ordered by defining u 21 to

**mean**that u ( E ) 22 ( E) for every E in the field determined by the closed sets . Similarly , the space C ( S

) is partially ordered by defining 1 g to

**mean**that f ( s ) g ( s ) for all s in S.Page 660

These results are applied to obtain , in Section 7 , corresponding

pointwise convergence theorems for the continuous case . Section 8 is

concerned with a certain class of operators T for which the sequence of averages

{ N - EN = 7 ...

These results are applied to obtain , in Section 7 , corresponding

**mean**andpointwise convergence theorems for the continuous case . Section 8 is

concerned with a certain class of operators T for which the sequence of averages

{ N - EN = 7 ...

### 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 | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains 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 Hilbert space 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