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 S1 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 S1 and an isometric algebraic isomorphism U between the algebras C ( S1 ) and A ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ