## Linear Operators: General theory |

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Results 1-3 of 26

Page 655

tv,w » 1 f (l-g-'M*+f)df _ TW(a;'5) = ^Ll-2^cos|+g-^ defines a strongly continuous

) ~ 2, xne > £B„ = — J aj(j)e-<n*t£». 18 Let 3£ = Lv{—n, n), 1 :g p < oo. Show that

...

tv,w » 1 f (l-g-'M*+f)df _ TW(a;'5) = ^Ll-2^cos|+g-^ defines a strongly continuous

**semi**-**group**on [0, co). Equivalently, 00 T(t)(x,s) = 2<r!nl<a;nein« — 00 OO If" if #(*) ~ 2, xne > £B„ = — J aj(j)e-<n*t£». 18 Let 3£ = Lv{—n, n), 1 :g p < oo. Show that

...

Page 694

f, -)|, 0 < a} in the lattice of //-measurable functions on S. Actually, in the following

theorem, which is a generalization of Theorem 7, the situation discussed is

somewhat more general than that of a fc-parameter

f, -)|, 0 < a} in the lattice of //-measurable functions on S. Actually, in the following

theorem, which is a generalization of Theorem 7, the situation discussed is

somewhat more general than that of a fc-parameter

**semi**-**group**for here we are ...Page 846

G Generalized sequence, definition and properties, 1.7.1-7 (20-29) Generator,

infinitesimal of a

theorem, II. 2. 4 (57) of an operator, II. 2.3 (57) Group, basic properties, 1. 10

definition ...

G Generalized sequence, definition and properties, 1.7.1-7 (20-29) Generator,

infinitesimal of a

**semigroup**of operators, VIII. 1.6 (619) Graph, closed graphtheorem, II. 2. 4 (57) of an operator, II. 2.3 (57) Group, basic properties, 1. 10

definition ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries 84 | 34 |

Copyright | |

80 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

a-finite 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 continuous linear functional convex set Corollary countably additive Definition denote dense Doklady Akad element equivalent everywhere exists finite dimensional follows from Theorem function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative non-zero normed linear space 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 valued function vector space weak topology weakly compact weakly sequentially compact zero