Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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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 ( A ; 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 ( μμn ; T + P ) ) clearly ...
... projections E ( A ; 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 ( μμn ; T + P ) ) clearly ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ 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