## Linear Operators: General theory |

### From inside the book

Results 1-3 of 85

Page 15

( b ) For every pair of distinct points x and y , there are

and y . ( c ) For every closed set A , and every x ¢ A , there are

neighborhoods of A and X . ( d ) For every pair of

there are ...

( b ) For every pair of distinct points x and y , there are

**disjoint**neighborhoods of xand y . ( c ) For every closed set A , and every x ¢ A , there are

**disjoint**neighborhoods of A and X . ( d ) For every pair of

**disjoint**closed sets A and B ,there are ...

Page 320

The semi - variation of the vector valued measure u is defined by 1 | el | ( E ) =

sup E q ; u ( E ; ) ] , EEE , where the supremum is taken over all finite collections

of scalars with Jalil s 1 and all partitions of E into a finite number of

E ...

The semi - variation of the vector valued measure u is defined by 1 | el | ( E ) =

sup E q ; u ( E ; ) ] , EEE , where the supremum is taken over all finite collections

of scalars with Jalil s 1 and all partitions of E into a finite number of

**disjoint**sets inE ...

Page 461

and an arbitrary convex set is possible , provided they are

Theorem 2 . 8 ) . He also proved that a convex set K which is compact in the X *

topology of the normed linear space X , can be separated from an arbitrary

closed ...

and an arbitrary convex set is possible , provided they are

**disjoint**( compareTheorem 2 . 8 ) . He also proved that a convex set K which is compact in the X *

topology of the normed linear space X , can be separated from an arbitrary

closed ...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

5 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 Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad domain elements 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 operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen semi-group 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