## Linear Operators: General theory |

### From inside the book

Results 1-3 of 79

Page 483

If T is

TS) is compact and hence closed in the s3)* topology of?)**. Thus if T is

...

If T is

**weakly compact**, then TS is compact in the 9)* topology of SJ) and thus x(TS) is compact and hence closed in the s3)* topology of?)**. Thus if T is

**weakly****compact**, (i) yields T**(Sj) Q x(TS). According to Theorem V.4.5, S1 = S**, and so...

Page 494

From IV. 10. 2 we conclude that T* maps the unit sphere of X* into a conditionally

Theorem 4.8 this implies that T is a

From IV. 10. 2 we conclude that T* maps the unit sphere of X* into a conditionally

**weakly compact**set of rca(S), and therefore T* is a**weakly compact**operator. ByTheorem 4.8 this implies that T is a

**weakly compact**operator. Q.E.D. 4 Theorem.Page 507

Let (S, Z, u) be a a- finite positive measure space, and let T be a

operator on L^S, Z, p) to a separable subset of the B-space 3c. Then there exists

a fi- essentially unique bounded measurable function x(-) on S to a weakly ...

Let (S, Z, u) be a a- finite positive measure space, and let T be a

**weakly compact**operator on L^S, Z, p) to a separable subset of the B-space 3c. Then there exists

a fi- essentially unique bounded measurable function x(-) on S to a weakly ...

### 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