## Linear Operators: General theory |

### From inside the book

Results 1-3 of 97

Page 844

fixed point of, V.10.8 (457) Equivalence of nornied linear spaces,

3.17 (65) Ergodic theorems, VII.7, VII.8.8-10 (598-599), VIII.4-8. (See also

Dominated theorems, Maximal theorems, Mean theorems, Point- wise theorems,

Uniform ...

fixed point of, V.10.8 (457) Equivalence of nornied linear spaces,

**definition**, II.3.17 (65) Ergodic theorems, VII.7, VII.8.8-10 (598-599), VIII.4-8. (See also

Dominated theorems, Maximal theorems, Mean theorems, Point- wise theorems,

Uniform ...

Page 846

G Generalized sequence,

infinitesimal of a semigroup of operators, VIII. 1.6 (619) Graph, closed graph

theorem, II.2.4 (57) of an operator, II.2.3 (57) Group, basic properties, 1.10

G Generalized sequence,

**definition**and properties, 1.7.1-7 (26-29) Generator,infinitesimal of a semigroup of operators, VIII. 1.6 (619) Graph, closed graph

theorem, II.2.4 (57) of an operator, II.2.3 (57) Group, basic properties, 1.10

**definition**, ...Page 856

6.22 (276) remarks on, (383) space,

of Boolean rings and algebras, I. 12.1 (41), (44) — Weierstrass theorem, IV. 6. 10

(272) complex case, IV. 0.17 (274) remarks on, (383-385) Strictly convex ...

6.22 (276) remarks on, (383) space,

**definition**, (398) theorems on representationof Boolean rings and algebras, I. 12.1 (41), (44) — Weierstrass theorem, IV. 6. 10

(272) complex case, IV. 0.17 (274) remarks on, (383-385) Strictly convex ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

44 other sections not shown

### 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

Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers contains continuous functions convex set Corollary countably additive Definition denote dense differential equations Doklady Akad Duke Math element equivalent exists finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lemma 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 properties proved real numbers reflexive Riesz Russian scalar semi-group sequentially compact Show simple functions subset subspace Suppose theory TM(S topological space Trans valued function Vber vector space weak topology weakly compact weakly sequentially compact zero