Linear Operators: Spectral operators |
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Page 2209
... uniformly closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed ...
... uniformly closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed ...
Page 2300
... uniformly bounded . Moreover , Σx- , ( E ( ^ „ ; T ) — E ( un ; T + P ) ) clearly converges uniformly for p≥ K and approaches zero in norm as p → ∞o . Since Σ , E ( λn ; T ) converges strongly ( T being spectral ) , it follows that ...
... uniformly bounded . Moreover , Σx- , ( E ( ^ „ ; T ) — E ( un ; T + P ) ) clearly converges uniformly for p≥ K and approaches zero in norm as p → ∞o . Since Σ , E ( λn ; T ) converges strongly ( T being spectral ) , it follows that ...
Page 2361
... uniformly bounded for λ in UN V1 , and hence , by the maximum modulus theorem , is uniformly bounded for A in i = NU1 • Since the set { U1 } , i≥ N , covers the whole plane , with the possible excep- tion of a bounded set , | F * ( A ) ...
... uniformly bounded for λ in UN V1 , and hence , by the maximum modulus theorem , is uniformly bounded for A in i = NU1 • Since the set { U1 } , i≥ N , covers the whole plane , with the possible excep- tion of a bounded set , | F * ( A ) ...
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