## Linear Operators: General theory |

### From inside the book

Results 1-3 of 84

Page 171

23

additive and bounded.

Show that E* contains every Borel set. 24

topological ...

23

**Suppose**that S is a metric space, that E is a cr-field, and that ft is countablyadditive and bounded.

**Suppose**that every continuous function is /^-measurable.Show that E* contains every Borel set. 24

**Suppose**that S is a compacttopological ...

Page 360

22

finite constant K such that for / in CBV, \(SJM\ ŁK(P(f. [0. 27t])+ sup IflaOl), 0 ^ X ^

271. 23

22

**Suppose**that (S„f)(x) -*•/(#) uniformly for every / in AC. Show that there exists afinite constant K such that for / in CBV, \(SJM\ ŁK(P(f. [0. 27t])+ sup IflaOl), 0 ^ X ^

271. 23

**Suppose**that (i) (S„f)(x) ->/(#) uniformly in x for / in AC. (ii) The ...Page 598

2 Let gn e JF(T), n = 1, 2

topology to a compact operator. Let X « a(T), and lim,,^^ g„(X) 0. Show that A is a

pole of a(T), and that E(X; T)S has a positive finite dimension. (Hint. See Exercise

...

2 Let gn e JF(T), n = 1, 2

**Suppose**that g„(T) converges in the uniform operatortopology to a compact operator. Let X « a(T), and lim,,^^ g„(X) 0. Show that A is a

pole of a(T), and that E(X; T)S has a positive finite dimension. (Hint. See Exercise

...

### 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 | 34 |

Copyright | |

79 other sections not shown

### Other editions - View all

### Common terms and phrases

a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed linear manifold compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations Doklady Akad element equivalent everywhere exists extended real valued extension fi(E finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality integral interval Lebesgue measure Lemma linear functional linear map linear operator linear topological space LP(S measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space uniformly unique v(fi valued function Vber vector valued weakly compact zero