## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 83

Page 280

That (1)

to show that condition (3) of that theorem

that S may be embedded as a dense subset of a compact Hausdorff space S, ...

That (1)

**implies**(2) can be proved in a manner similar to that used in Theorem 14to show that condition (3) of that theorem

**implies**(4). From Corollary 19 it followsthat S may be embedded as a dense subset of a compact Hausdorff space S, ...

Page 430

We observe first that each of the three conditions

metric topology, for a "(A) is a bounded set of scalars for each aro e &" and we

can apply II.3.20. It is readily seen that (iii)

We observe first that each of the three conditions

**implies**that A is bounded in themetric topology, for a "(A) is a bounded set of scalars for each aro e &" and we

can apply II.3.20. It is readily seen that (iii)

**implies**(ii). The other implications we ...Page 454

To each point p e C there corresponds a unique nearest point N(p) e K. To see

this, note that Lemma IV.4.2

p-k, - inf, .kp —k then {k} converges, say, to qe K. If{k} is another such minimizing

...

To each point p e C there corresponds a unique nearest point N(p) e K. To see

this, note that Lemma IV.4.2

**implies**that if {k, is a sequence in K such that lim, ...p-k, - inf, .kp —k then {k} converges, say, to qe K. If{k} is another such minimizing

...

### 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