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 netrospect 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 netrospect 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 continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ