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 ) = ( AX ) ...
... 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 ) = ( AX ) ...
Page 2198
... projections . A projection F is an upper bound for { E } if and only if it is an upper bound for { F } , and since .. n P ( UX ) ( E1V · · · VE2 ) X = sp 1 for any finite set of projections , to construct a least upper bound for { E } ...
... projections . A projection F is an upper bound for { E } if and only if it is an upper bound for { F } , and since .. n P ( UX ) ( E1V · · · VE2 ) X = sp 1 for any finite set of projections , to construct a least upper bound for { E } ...
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 ...
... 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 ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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