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 . PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean algebra ...
... projections in a o - complete Boolean algebra of projections in a B - space converges weakly to a projection , then it converges strongly . PROOF . In view of Lemma 23 , the proof may be restricted to the case where the Boolean algebra ...
Page 2300
... projections E ( λn ; 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 , Σ % - , ( E ( ^ „ ; T ) — E ( un ; T + P ) ) clearly ...
... projections E ( λn ; 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 , Σ % - , ( E ( ^ „ ; T ) — E ( un ; T + P ) ) clearly ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero