## Linear Operators: General theory |

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Page 95

In some cases that will be encountered the values of ft are not scalars, but

customarily where integration is used in this text p is a scalar

/ a vector (or scalar)

defined ...

In some cases that will be encountered the values of ft are not scalars, but

customarily where integration is used in this text p is a scalar

**valued function**and/ a vector (or scalar)

**valued function**. Thus, even if the integration process isdefined ...

Page 119

(b) the

measurable. Next suppose that we consider a

(b) the

**function**g defined by g(s) = f(s) if s 4 S+ \j S~, g(s) = 0 if s e S+ U S~, is //-measurable. Next suppose that we consider a

**function**/ (vector or extended real-**valued**) which is defined only on the complement of a //-null set NQS. Then we ...Page 196

Next we study the relation between the theory of product measures and the

theory of vector

F is a yw-measurable

each ...

Next we study the relation between the theory of product measures and the

theory of vector

**valued**integrals. ... Suppose that (S, Z, fi) is a measure space andF is a yw-measurable

**function**whose values are in L„(T, ZT, X), 1 ^ p < oo. Foreach ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

78 other sections not shown

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additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive Definition denote dense differential equations disjoint Doklady Akad Duke Math element ergodic theorem exists finite dimensional function defined Hausdorff space Hence Hilbert space homeomorphism ibid inequality integral Lebesgue Lebesgue measure Lemma linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc Proof properties proved real numbers reflexive Riesz Russian Sbornik N. S. scalar self-adjoint semi-group sequentially compact Show simple functions spectral Studia Math subset subspace Suppose theory topological space Trans uniformly Univ valued function Vber vector space weak topology weakly compact zero