## Linear Operators: General theory |

### From inside the book

Results 1-3 of 35

Page 161

ji e ba. For e > 0 choose n, so that \ftn— fim\ ^eform.n^n,. Then fi(E)—fin(E) = lim,^

,,, (fj,m(E)—/u„(E)), from which it follows that \ft—/in\ e for n ^ Hence fj,n -> p,

which proves that

...

ji e ba. For e > 0 choose n, so that \ftn— fim\ ^eform.n^n,. Then fi(E)—fin(E) = lim,^

,,, (fj,m(E)—/u„(E)), from which it follows that \ft—/in\ e for n ^ Hence fj,n -> p,

which proves that

**ba**(**S**, Z, 36) is complete. It follows, therefore, that**ba**(**S**,Z,£) is a...

Page 311

The space

also weakly complete. Proof. Consider the closed subspace B(S, Z) of B(S).

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1

such that ...

The space

**ba**(**S**,Z) is weakly complete. If S is a topological space, the rba(S) isalso weakly complete. Proof. Consider the closed subspace B(S, Z) of B(S).

According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1

such that ...

Page 340

16 Let S be a completely regular topological space. Show that C(S) is separable

if and only if S is compact and metric. 17 Show that a sequence {A„} of elements

of

16 Let S be a completely regular topological space. Show that C(S) is separable

if and only if S is compact and metric. 17 Show that a sequence {A„} of elements

of

**ba**(**S**, E) converge weakly to an element X e**ba**(**S**, E) if and only if there exists ...### 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 | |

78 other sections not shown

### Other editions - View all

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc Proof properties proved real numbers reflexive Riesz Russian Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero