Linear Operators: Spectral operators |
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Page 1928
... projections A and B in X are the projections AB and A + B − AB , respectively . The ranges of the inter- section and union of two commuting projections are given by the equa- tions - ( A / B ) X = ( AX ) ~ ( BX ) , ( A \ B ) ( X ) ...
... projections A and B in X are the projections AB and A + B − AB , respectively . The ranges of the inter- section and union of two commuting projections are given by the equa- tions - ( A / B ) X = ( AX ) ~ ( BX ) , ( A \ B ) ( X ) ...
Page 2218
... projections in a o - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . α PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean ...
... projections in a o - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . α PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean ...
Page 2300
... projections E ( λ , ; T ) is uniformly bounded , it is clear from [ * ] that the collection of finite sums of projections E ( μn ; T + P ) , n ≥ K , is uniformly bounded . Moreover , Σx- , ( E ( ^ „ ; T ) — E ( un ; T + P ) ) clearly ...
... projections E ( λ , ; T ) is uniformly bounded , it is clear from [ * ] that the collection of finite sums of projections E ( μn ; T + P ) , n ≥ K , is uniformly bounded . Moreover , Σx- , ( E ( ^ „ ; T ) — E ( un ; T + P ) ) clearly ...
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