Linear Operators: General theory |
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Page 743
... transformations in Hilbert space . Duke J. Math . 7 , 504-508 ( 1940 ) . Cameron , R. H. 1. A " Simpson's Rule " for the numerical evaluation of Wiener's integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . The first ...
... transformations in Hilbert space . Duke J. Math . 7 , 504-508 ( 1940 ) . Cameron , R. H. 1. A " Simpson's Rule " for the numerical evaluation of Wiener's integrals in function space . Duke Math . J. 18 , 111-130 ( 1951 ) . 2 . The first ...
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
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ