Linear Operators: General theory |
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Page 611
... Perturbation theory . The questions of perturbation theory go back to the work of Lord Rayleigh and E. Schrödinger , but it is Rellich who developed the theory along the lines presented here . ( For an expository paper on this theory ...
... Perturbation theory . The questions of perturbation theory go back to the work of Lord Rayleigh and E. Schrödinger , but it is Rellich who developed the theory along the lines presented here . ( For an expository paper on this theory ...
Page 772
... perturbation method . J. Fac . Sci . Univ . Tokyo Sect . I. 6 , 145-226 ( 1951 ) . Perturbation theory of semi - bounded operators . Math . Ann . 125 , 435–447 ( 1953 ) . On the perturbation theory of closed linear operators . J. Math ...
... perturbation method . J. Fac . Sci . Univ . Tokyo Sect . I. 6 , 145-226 ( 1951 ) . Perturbation theory of semi - bounded operators . Math . Ann . 125 , 435–447 ( 1953 ) . On the perturbation theory of closed linear operators . J. Math ...
Page 852
... Perturbation of bounded linear opera- tors , remarks on , ( 611-612 ) study of , VII.6 , VII.8.1-2 ( 597– 598 ) , VII.8.4-5 ( 598 ) Perturbation of infinitesimal generator of a semigroup , ( 630-639 ) Phillips ' perturbation theorem ...
... Perturbation of bounded linear opera- tors , remarks on , ( 611-612 ) study of , VII.6 , VII.8.1-2 ( 597– 598 ) , VII.8.4-5 ( 598 ) Perturbation of infinitesimal generator of a semigroup , ( 630-639 ) Phillips ' perturbation theorem ...
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