Linear Operators: General theory |
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Page v
... ( Chapter XIII ) of the spectral theory of ordinary self - adjoint differen- tial operators is presented , while on the other hand the theory of local- ly convex spaces is treated ( Chapter V ) rather briefly in its connection with the ...
... ( Chapter XIII ) of the spectral theory of ordinary self - adjoint differen- tial operators is presented , while on the other hand the theory of local- ly convex spaces is treated ( Chapter V ) rather briefly in its connection with the ...
Page vii
... chapter . In the course of Chapter XI , this lemma is referred to as Lemma 5.4 , and in the course of the fifth sec- tion of Chapter XI it is referred to as Lemma 4 . The general character of the present work may be indicated by a brief ...
... chapter . In the course of Chapter XI , this lemma is referred to as Lemma 5.4 , and in the course of the fifth sec- tion of Chapter XI it is referred to as Lemma 4 . The general character of the present work may be indicated by a brief ...
Page viii
Nelson Dunford, Jacob T. Schwartz. close to Chapter XIII , and also discusses some points of the theory given in Chapter XIX . Surveying in retrospect the theories presented in the following twenty chapters , it seems to the authors that ...
Nelson Dunford, Jacob T. Schwartz. close to Chapter XIII , and also discusses some points of the theory given in Chapter XIX . Surveying in retrospect the theories presented in the following twenty chapters , it seems to the authors that ...
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 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ