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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Results 1-3 of 92
Page 2174
... Hence we have 1 | ett ( S + T ) | = | eitsettт | ≤etts || ettr | ≤ M1M2 for all te R. Hence if this boundedness implied that S + T was a spectral operator , we would have a contradiction to McCarthy's [ 2 , I ] modification of ...
... Hence we have 1 | ett ( S + T ) | = | eitsettт | ≤etts || ettr | ≤ M1M2 for all te R. Hence if this boundedness implied that S + T was a spectral operator , we would have a contradiction to McCarthy's [ 2 , I ] modification of ...
Page 2295
... Hence f ( T ) E ( o ; T ) is the inverse of ( μIT ) E ( o ; T ) X , which shows that o ( T | E ( o ; T ) X ) ≤ 0 . Suppose next that E ( σ ; T ) = 0 , but that σ is not void . Then E ( λ ; T ) = E ( o ; T ) = E ( λ ; T ) E ( σ ; T ) ...
... Hence f ( T ) E ( o ; T ) is the inverse of ( μIT ) E ( o ; T ) X , which shows that o ( T | E ( o ; T ) X ) ≤ 0 . Suppose next that E ( σ ; T ) = 0 , but that σ is not void . Then E ( λ ; T ) = E ( o ; T ) = E ( λ ; T ) E ( σ ; T ) ...
Page 2357
... Hence ( P + N ) ( S− \ I ) -v = P ( S –AI ) - " + N ( S – MI ) - = - = P ( T − XI ) -L + N ( S –AI ) -v ν V = is a bounded operator which is compact if P ( TAI ) is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) of the ...
... Hence ( P + N ) ( S− \ I ) -v = P ( S –AI ) - " + N ( S – MI ) - = - = P ( T − XI ) -L + N ( S –AI ) -v ν V = is a bounded operator which is compact if P ( TAI ) is compact ( cf. VI.5.4 ) . In all cases ( a ) , ( b ) , ( c ) of the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
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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