Linear Operators: Spectral operators |
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Page 2249
... Theorem 9 ( v ) that ( 1 / ƒ ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( ƒ ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
... Theorem 9 ( v ) that ( 1 / ƒ ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( ƒ ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
Page 2403
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
Page 2418
... theorem ( III.11.14 ) , the integral ( 75 ) SS141 ( 2 , 2 ) | D | A2 ( z , z ' ) | | zz | f ( z ) dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ( A1 ) ...
... theorem ( III.11.14 ) , the integral ( 75 ) SS141 ( 2 , 2 ) | D | A2 ( z , z ' ) | | zz | f ( z ) dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ( A1 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero