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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ