Linear Operators: General theory |
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... formal concept of the adjoint operator goes back to matrix theory and to the theories of differential and integral equations . In the spaces Lp , p > 1 , and l2 , Riesz [ 2 ; p . 478 , 6 ; p . 85 ] made use of this notion and proved the ...
... formal concept of the adjoint operator goes back to matrix theory and to the theories of differential and integral equations . In the spaces Lp , p > 1 , and l2 , Riesz [ 2 ; p . 478 , 6 ; p . 85 ] made use of this notion and proved the ...
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