Linear Operators: General theory |
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Page 569
... THEOREM . ( Spectral mapping theorem . ) If f is in F ( T ) , then f ( o ( T ) ) = o ( f ( T ) ) . PROOF . Let e σ ( T ) , and VII.3.11 569 FUNCTIONS OF AN OPERATOR Functions of an Operator.
... THEOREM . ( Spectral mapping theorem . ) If f is in F ( T ) , then f ( o ( T ) ) = o ( f ( T ) ) . PROOF . Let e σ ( T ) , and VII.3.11 569 FUNCTIONS OF AN OPERATOR Functions of an Operator.
Page 604
... spectral mapping theorem to polynomials in T. 10 THEOREM . If P is a polynomial , P ( o ( T ) ) = σ ( P ( T ) ) . = PROOF . Let P be of degree n , and suppose λ & P ( σ ( T ) ) . If g ( § ) = [ λ − P ( § ) ] − 1 , g is in F ( T ) ...
... spectral mapping theorem to polynomials in T. 10 THEOREM . If P is a polynomial , P ( o ( T ) ) = σ ( P ( T ) ) . = PROOF . Let P be of degree n , and suppose λ & P ( σ ( T ) ) . If g ( § ) = [ λ − P ( § ) ] − 1 , g is in F ( T ) ...
Page 780
... spectral theorem of self - adjoint operators . Acta Sci . Math . Szeged 9 , 174-186 ( 1939 ) . 2 . Bounded self - adjoint operators and the problem of moments . Bull . Amer . Math . Soc . 45 , 303-306 ( 1939 ) . Lengyel , B. A. , and ...
... spectral theorem of self - adjoint operators . Acta Sci . Math . Szeged 9 , 174-186 ( 1939 ) . 2 . Bounded self - adjoint operators and the problem of moments . Bull . Amer . Math . Soc . 45 , 303-306 ( 1939 ) . Lengyel , B. A. , and ...
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