## Linear Operators: General theory |

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Page 838

space of, definition, IV.2.24 (242)

Arzela theorem, on continuity of limit function, IV.6.11 (268) remarks concerning, (

383) Ascoli-Arzela theorem, on compactness of continuous functions, IV.6.7 ...

space of, definition, IV.2.24 (242)

**properties**, IV.15 Annihilator of a set, II.4.17 (72)Arzela theorem, on continuity of limit function, IV.6.11 (268) remarks concerning, (

383) Ascoli-Arzela theorem, on compactness of continuous functions, IV.6.7 ...

Page 840

14 Closed set, definition, 1.4.8 (10)

70) Closed unit sphere, U.S.] (59) Closure of a set, criterion to be in, 1.7.2 (27)

definition, 1.4.0 (11)

...

14 Closed set, definition, 1.4.8 (10)

**properties**, 1.4.4-5 (10) Closed sphere, II.4.1 (70) Closed unit sphere, U.S.] (59) Closure of a set, criterion to be in, 1.7.2 (27)

definition, 1.4.0 (11)

**properties**of the closure operation, 1.4.10-11 (11-12) Cluster...

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2.5 (478), (554) Extremal point and subset, definitions V.8.1 (439) examples and

disconnected, (398) F F-space, basic

2.5 (478), (554) Extremal point and subset, definitions V.8.1 (439) examples and

**properties**, V.ll.1-0 (457-458) remarks on, (400), (473) study of, V.8 Extremallydisconnected, (398) F F-space, basic

**properties**, 11.1-2 definition, II.1.10 (51) ...### 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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### 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