## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 91

Page 838

space of, definition, IV.2.24 (242)

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

383) Ascoli-Arzelā 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)Arzelā theorem, on continuity of limit function, IV.6.11 (268) remarks concerning, (

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

Page 840

Closed orthonormal system, definition, IV.14.1 (357) study of, IV.14 Closed set,

definition, I.4.3 (10)

sphere, II.3.1 (59) Closure of a set, criterion to be in, I.7.2 (27) definition, I.4.9 (11)

...

Closed orthonormal system, definition, IV.14.1 (357) study of, IV.14 Closed set,

definition, I.4.3 (10)

**properties**, I.4.4–5 (10) Closed sphere, II.4.1 (70) Closed unitsphere, II.3.1 (59) Closure of a set, criterion to be in, I.7.2 (27) definition, I.4.9 (11)

...

Page 844

... definition, (229) Essential supremum, definition, III.1.11 (100–101) Essentially

bounded, definition, III.1.11 (100–101) Essentially separably valued, definition, III.

1.11 (100–101) Euclidean space, definition, IV.2.1 (238) further

...

... definition, (229) Essential supremum, definition, III.1.11 (100–101) Essentially

bounded, definition, III.1.11 (100–101) Essentially separably valued, definition, III.

1.11 (100–101) Euclidean space, definition, IV.2.1 (238) further

**properties**, IV.15...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

### Common terms and phrases

additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſš linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero