Linear Operators: General theory |
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Page 542
... representations were given in Sections 7-8 . For the convenience of the reader , we have tabulated here references to the literature where such representation theorems are explicitly stated . There are four tables ; one for the general ...
... representations were given in Sections 7-8 . For the convenience of the reader , we have tabulated here references to the literature where such representation theorems are explicitly stated . There are four tables ; one for the general ...
Page 552
... representation of linear operators is that dealing with the representation of linear functions defined on certain spaces with values in a B - space . Gowurin gave a representa- tion for the general bounded linear functional on the space ...
... representation of linear operators is that dealing with the representation of linear functions defined on certain spaces with values in a B - space . Gowurin gave a representa- tion for the general bounded linear functional on the space ...
Page 733
... Representation of functionals by integrals . Duke Math . J. 17 , 499–506 ( 1950 ) . 4. Approximation in , and representation of , certain Banach algebras . Amer . J. Math . 71 , 763-790 ( 1949 ) . 5 . 6 . 8 . A topology for spaces of ...
... Representation of functionals by integrals . Duke Math . J. 17 , 499–506 ( 1950 ) . 4. Approximation in , and representation of , certain Banach algebras . Amer . J. Math . 71 , 763-790 ( 1949 ) . 5 . 6 . 8 . A topology for spaces of ...
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