Linear Operators: Spectral operators |
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Page 2174
... hence is a scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded ... Hence we have 1 2 lett ( S + T ) | = lettsettr | ≤ | etts || ettT | ≤ M1M1⁄2 1 for all tЄ R. Hence if this ...
... hence is a scalar type operator with real spectrum . ( This follows from Lemma XV.6.1 which implies that the bounded ... Hence we have 1 2 lett ( S + T ) | = lettsettr | ≤ | etts || ettT | ≤ M1M1⁄2 1 for all tЄ R. Hence if this ...
Page 2295
... Hence E ( σ ; T ) X is at least k - dimen- sional . This proves the remainder of the present lemma . Q.E.D. 4 DEFINITION . Let T be an unbounded discrete operator in the B - space X , with spectrum { \ , } . If E ( λ¡ ; T ) = E ( λ ...
... Hence E ( σ ; T ) X is at least k - dimen- sional . This proves the remainder of the present lemma . Q.E.D. 4 DEFINITION . Let T be an unbounded discrete operator in the B - space X , with spectrum { \ , } . If E ( λ¡ ; T ) = E ( λ ...
Page 2357
... Hence ( P + N ) ( S – XI ) — ' — P ( S — \ I ) − ” + N ( S — \ I ) ̄ ” = = P ( T − XI ) - L + N ( S − XI ) -v = - ν is a bounded operator which is compact if P ( T - I ) is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) ...
... Hence ( P + N ) ( S – XI ) — ' — P ( S — \ I ) − ” + N ( S — \ I ) ̄ ” = = P ( T − XI ) - L + N ( S − XI ) -v = - ν is a bounded operator which is compact if P ( T - I ) is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) ...
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