## Linear Operators: General theory |

### From inside the book

Results 1-3 of 65

Page 18

A continuous one-to-one map from a compact space to a

homeomorphism. Proof. Let X be a compact space, Y a

one-to-one continuous function on X, with f(X) = Y. According to the preceding ...

A continuous one-to-one map from a compact space to a

**Hausdorff space**is ahomeomorphism. Proof. Let X be a compact space, Y a

**Hausdorff space**, and / aone-to-one continuous function on X, with f(X) = Y. According to the preceding ...

Page 274

Let S be a compact

continuous functiom on S. Let % be a closed subalgebra of C(S) which contains

the unit e and contains, with f, its complex conjugate J defined by f(s) = f(s). Then

21 ...

Let S be a compact

**Hausdorff space**and C(S) be tlie algebra of all complexcontinuous functiom on S. Let % be a closed subalgebra of C(S) which contains

the unit e and contains, with f, its complex conjugate J defined by f(s) = f(s). Then

21 ...

Page 276

Suppose, in addition to the hypotheses of Theorem 18, that the functions of 91

distinguish between tlie points of S. Then there exists a compact

S1 and a one-to-ane embedding of S as a dense subset of St such that each f in ...

Suppose, in addition to the hypotheses of Theorem 18, that the functions of 91

distinguish between tlie points of S. Then there exists a compact

**Hausdorff space**S1 and a one-to-ane embedding of S as a dense subset of St such that each f in ...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### 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 compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional 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 Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact