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 1
... theory , topology and algebra . Chapter I discusses all of the concepts and results of these theories which will be used in this text . The exposition is complete , but brief ; it contains results and proofs , with little accompanying ...
... theory , topology and algebra . Chapter I discusses all of the concepts and results of these theories which will be used in this text . The exposition is complete , but brief ; it contains results and proofs , with little accompanying ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ