Linear Operators: General theory |
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Page 224
... complex valued analytic functions of one complex variable and this theory will be applied here to obtain the extensions which will be used later . Throughout this section , will denote a complex B - space . DEFINITION . Let G be an open ...
... complex valued analytic functions of one complex variable and this theory will be applied here to obtain the extensions which will be used later . Throughout this section , will denote a complex B - space . DEFINITION . Let G be an open ...
Page 238
... complex valued functions f . g defined on a specified domain S. Here , addition and multiplication are understood to ... complex valued functions with these properties . Unless the con- trary is specified , both possibilities are ...
... complex valued functions f . g defined on a specified domain S. Here , addition and multiplication are understood to ... complex valued functions with these properties . Unless the con- trary is specified , both possibilities are ...
Page 274
... complex algebra B ( S ) containing the unit e as well as the complex conjugate of each of its elements . Then there exists a compact Hausdorff space S , and an isometric algebraic isomorphism U between the algebras C ( S1 ) and A ...
... complex algebra B ( S ) containing the unit e as well as the complex conjugate of each of its elements . Then there exists a compact Hausdorff space S , and an isometric algebraic isomorphism U between the algebras C ( S1 ) and A ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ