## Linear Operators: General theory |

### From inside the book

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Page 56

Since the map y -> is a

V. Thus, TG 2 TM-TM □ TM-TM 2 F-F. Since a map of the form y -*□ a— y is a

Since the map y -> is a

**homeomorphism**in 'J), TAf contains a non-void open setV. Thus, TG 2 TM-TM □ TM-TM 2 F-F. Since a map of the form y -*□ a— y is a

**homeomorphism**, the set a — V is open. Since the set V— V = (J (a — F) is the ...Page 91

However, Kolmogoroff [1] proved that a topological linear space is

convex neighborhood of the origin. Wehausen [1] showed that if a topological

linear space has a ...

However, Kolmogoroff [1] proved that a topological linear space is

**homeomorphic**to a normed linear space if and only if there exists a boundedconvex neighborhood of the origin. Wehausen [1] showed that if a topological

linear space has a ...

Page 442

Q ?'s « compart Hausdorff space, and C(Q) is the B-space of all real or complex

continuous functions on Q, then the mapping X : q -> x* of Q into a subset Q of the

extremal points of S* is a

Q ?'s « compart Hausdorff space, and C(Q) is the B-space of all real or complex

continuous functions on Q, then the mapping X : q -> x* of Q into a subset Q of the

extremal points of S* is a

**homeomorphism**where C*(Q) has its C(Q) topology.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### 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