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Page 761
... transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . 5. Measure Theory . D. Van Nostrand , New York , 1950 . 6. Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . 7 ...
... transformations . Bull . Amer . Math . Soc . 55 , 1015–1034 ( 1949 ) . 5. Measure Theory . D. Van Nostrand , New York , 1950 . 6. Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . 7 ...
Page 783
... transformations in certain vector spaces . Bull . Amer . Math . Soc . 45 , 564-569 ( 1939 ) . On a calculus of ... transformations in reflexive vector spaces . Trans . Amer . Math . Soc . 49 , 18-40 ( 1941 ) . Means of iterated ...
... transformations in certain vector spaces . Bull . Amer . Math . Soc . 45 , 564-569 ( 1939 ) . On a calculus of ... transformations in reflexive vector spaces . Trans . Amer . Math . Soc . 49 , 18-40 ( 1941 ) . Means of iterated ...
Page 814
... transformations autoadjointes dans l'espace de Hilbert . Comment . Math . Helv . 19 , 347-366 ( 1946-1947 ) . On the set of positive functions in L. Ann . of Math . ( 2 ) 39 , 1-13 ( 1938 ) . On semi - groups of self - adjoint ...
... transformations autoadjointes dans l'espace de Hilbert . Comment . Math . Helv . 19 , 347-366 ( 1946-1947 ) . On the set of positive functions in L. Ann . of Math . ( 2 ) 39 , 1-13 ( 1938 ) . On semi - groups of self - adjoint ...
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