Linear Operators: General theory |
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Page v
... theory of linear operations , together with a survey of the application of this general theory to the diverse fields of more classical analysis . It has been our desire to emphasize the significance of the relationships between the ...
... theory of linear operations , together with a survey of the application of this general theory to the diverse fields of more classical analysis . It has been our desire to emphasize the significance of the relationships between the ...
Page viii
... theory given in Chapter XIX . Surveying in netrospect the theories presented in the following twenty chapters , it seems to the authors that the general theory of the first seven chapters , and the Hilbert space theory of self - adjoint ...
... theory given in Chapter XIX . Surveying in netrospect the theories presented in the following twenty chapters , it seems to the authors that the general theory of the first seven chapters , and the Hilbert space theory of self - adjoint ...
Page 611
... theory . The questions of perturbation theory go back to the work of Lord Rayleigh and E. Schrödinger , but it is Rellich who developed the theory along the lines presented here . ( For an expository paper on this theory , see Rellich ...
... theory . The questions of perturbation theory go back to the work of Lord Rayleigh and E. Schrödinger , but it is Rellich who developed the theory along the lines presented here . ( For an expository paper on this theory , see Rellich ...
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