Linear Operators: Spectral operators |
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Page 2292
... finite limit point ; ( b ) the resolvent R ( A ; T ) is compact for every λ o ( T ) ; ( c ) every λo in o ( T ) is a pole of finite order v ( o ) of the resolvent and if , for some positive integer k , f satisfies the equation then f ...
... finite limit point ; ( b ) the resolvent R ( A ; T ) is compact for every λ o ( T ) ; ( c ) every λo in o ( T ) is a pole of finite order v ( o ) of the resolvent and if , for some positive integer k , f satisfies the equation then f ...
Page 2300
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I — E2 ) = 0 if μ is ...
... finite dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I — E2 ) = 0 if μ is ...
Page 2469
... finite , and that | V ‹ ) | * < ɛ . Thus the proof of our lemma is complete . Q.E.D. - Next we prove an important inequality . - - 17 LEMMA . Suppose that we call on element ƒ H ' very smooth and finite if ( i ) there exists an integer ...
... finite , and that | V ‹ ) | * < ɛ . Thus the proof of our lemma is complete . Q.E.D. - Next we prove an important inequality . - - 17 LEMMA . Suppose that we call on element ƒ H ' very smooth and finite if ( i ) there exists an integer ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero