Linear Operators: General theory |
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Page 790
... transformations . Bull . Amer . Math . Soc . 48 , 76-93 ( 1942 ) . Linear transformations between Hilbert spaces and the application of this theory to linear partial differential equations . Trans . Amer . Math . Soc . 37 , 301-338 ...
... transformations . Bull . Amer . Math . Soc . 48 , 76-93 ( 1942 ) . Linear transformations between Hilbert spaces and the application of this theory to linear partial differential equations . Trans . Amer . Math . Soc . 37 , 301-338 ...
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 ...
Page 826
... transformations and their resolvents in Orlicz and Lebesgue spaces . Compositio Math . 10 , 56-94 ( 1952 ) . 3. Normalisable transformations in Hilbert space and systems of linear integral equations . Acta Math . 83 , 197-248 ( 1950 ) ...
... transformations and their resolvents in Orlicz and Lebesgue spaces . Compositio Math . 10 , 56-94 ( 1952 ) . 3. Normalisable transformations in Hilbert space and systems of linear integral equations . Acta Math . 83 , 197-248 ( 1950 ) ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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