Linear Operators: General theory |
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Page 684
... resolved by a reduction to the study of the averages of the iterates of a single operator . It will not be necessary to restrict the discussion to the type of semi - group arising in classical statistical mechanics as the results to be ...
... resolved by a reduction to the study of the averages of the iterates of a single operator . It will not be necessary to restrict the discussion to the type of semi - group arising in classical statistical mechanics as the results to be ...
Page 749
... Resolution of the identity for commutative B * -algebras of operators . Acta Sci . Math . Szeged 12 Pars B , 51-56 ( 1950 ) . 14. Spectral theory in abstract spaces and Banach algebras . Proc . Symposium on Spectral Theory and ...
... Resolution of the identity for commutative B * -algebras of operators . Acta Sci . Math . Szeged 12 Pars B , 51-56 ( 1950 ) . 14. Spectral theory in abstract spaces and Banach algebras . Proc . Symposium on Spectral Theory and ...
Page 806
... resolution for operators in Hilbert space . Dissertation , University of Chicago , 1955 . Schreier , J. 1. Ein Gegenbeispiel zur Theorie der schwachen Konvergenz . Studia Math . 2 , 2 , 58-62 ( 1930 ) . Schreier , O. 1. Abstrakte ...
... resolution for operators in Hilbert space . Dissertation , University of Chicago , 1955 . Schreier , J. 1. Ein Gegenbeispiel zur Theorie der schwachen Konvergenz . Studia Math . 2 , 2 , 58-62 ( 1930 ) . Schreier , O. 1. Abstrakte ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ