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 vi
Nelson Dunford, Jacob T. Schwartz. theory of spaces and operators , and all material pertaining to the spectral theory of arbitrary operators into the first part ; all material relating to the theory of completely reducible operators ...
Nelson Dunford, Jacob T. Schwartz. theory of spaces and operators , and all material pertaining to the spectral theory of arbitrary operators into the first part ; all material relating to the theory of completely reducible operators ...
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 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ