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 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ