## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 89

Page 20

If every Cauchy sequence is convergent, a metric space is said to be

The next three lemmas are immediate consequences of the definitions. 6 LEMMA

. In a metric space, a convergent sequence is a Cauchy sequence. A Cauchy ...

If every Cauchy sequence is convergent, a metric space is said to be

**complete**.The next three lemmas are immediate consequences of the definitions. 6 LEMMA

. In a metric space, a convergent sequence is a Cauchy sequence. A Cauchy ...

Page 311

The space ba(S, X) is weakly

also weakly

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S,

such ...

The space ba(S, X) is weakly

**complete**. If S is a topological space, the rba (S) isalso weakly

**complete**. PRoof. Consider the closed subspace B(S, X) of B(S).According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S,

such ...

Page 840

Hilbert space, IV.4.8 (250)

**Complete**metric I.6.15 (22) definition, I.6.5 (19) properties, I.6.7 (20), I.6.9 (20)**Complete**normed linear space. (See B-space)**Complete**orthonormal set, inHilbert space, IV.4.8 (250)

**Complete**partially ordered definition, I.3.9 (8) ...### What people are saying - Write a review

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

### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Other editions - View all

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero