## Linear Operators: General theory |

### From inside the book

Results 1-3 of 78

Page 186

Thus, the field <P of Lemma 1 is a cr-field and the measure // of Lemma 1 is

countably additive on 0. Consequently, the ... Let (S,E,/i) be the product of finite

S2 the ...

Thus, the field <P of Lemma 1 is a cr-field and the measure // of Lemma 1 is

countably additive on 0. Consequently, the ... Let (S,E,/i) be the product of finite

**positive measure spaces**(Sv E1, fa) and (S2, E2, u2). For each E in E and s2 inS2 the ...

Page 302

We now append some properties of the space Lp which spring from its natural

ordering, and which will be useful later. ... Let (S, E, ft) be a

We now append some properties of the space Lp which spring from its natural

ordering, and which will be useful later. ... Let (S, E, ft) be a

**positive measure****space**. ... may therefore suppose that (S, E, /u) is a <r-finite**positive measure****space**.Page 725

1 "-1 lim sup - 2 /i,((p~'e) ^ Kji(e) n->oo n } =0 for each set e of finite //-measure. (

Hint. Consider the map f(s) -> %A{s)f((ps) for each A e 27 with //(v4) < co.) 37 Let (

S, E, //) be a

...

1 "-1 lim sup - 2 /i,((p~'e) ^ Kji(e) n->oo n } =0 for each set e of finite //-measure. (

Hint. Consider the map f(s) -> %A{s)f((ps) for each A e 27 with //(v4) < co.) 37 Let (

S, E, //) be a

**positive measure space**, and T a non-negative linear transformation...

### 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