## Linear Operators: General theory |

### From inside the book

Results 1-3 of 48

Page 341

Show that a set K C ba(S, E) is conditionally compact if and only if (i) K is

bounded. ... 22 Let S be a normal topological space and rca(S) the regular

countably additive set functions on the field of

is weakly ...

Show that a set K C ba(S, E) is conditionally compact if and only if (i) K is

bounded. ... 22 Let S be a normal topological space and rca(S) the regular

countably additive set functions on the field of

**Borel sets**in S. Prove that (i) rca(S)is weakly ...

Page 492

In the following, 3B denotes the field of

by the closed sets of S. If /< is a function on 33 with values in a Zf-space, then as

in Definition IV. 10.8, the symbol denotes the semi-variation of fi over E e 33 and

...

In the following, 3B denotes the field of

**Borel sets**in S, i.e., the <r-field generatedby the closed sets of S. If /< is a function on 33 with values in a Zf-space, then as

in Definition IV. 10.8, the symbol denotes the semi-variation of fi over E e 33 and

...

Page 516

39 Let S be a compact Hausdorff space and <f> a continuous function on S to S.

Show that there is a regular countably additive non-negative measure fi defined

for all

39 Let S be a compact Hausdorff space and <f> a continuous function on S to S.

Show that there is a regular countably additive non-negative measure fi defined

for all

**Borel sets**in S with the properties that fi is not identically zero and /j, ...### 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 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

### Other editions - View all

### Common terms and phrases

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero