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 1926
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined . by the equations N = T - Σ λε ( λ ) , E ...
... arbitrary T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite them by introducing the nilpotent N and the resolution of the identity E defined . by the equations N = T - Σ λε ( λ ) , E ...
Page 1941
... arbitrary , it follows that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent . Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral operator TS + N into a sum of a scalar type ...
... arbitrary , it follows that o ( N ) = { 0 } . It then follows from Corollary 3 that N is a quasi - nilpotent . Q.E.D. 6 DEFINITION . The decomposition , given in Theorem 5 , of a spectral operator TS + N into a sum of a scalar type ...
Page 1963
... arbitrary , shows that by = ay . Since B ( S ) is a B * -algebra ( IX.3.2 ) under the involution A → A * , it follows that the map ( a ,, ) → ( b1 , ) is an involution in the algebra M , ( B ( H ) ) and that , with this involution , M ...
... arbitrary , shows that by = ay . Since B ( S ) is a B * -algebra ( IX.3.2 ) under the involution A → A * , it follows that the map ( a ,, ) → ( b1 , ) is an involution in the algebra M , ( B ( H ) ) and that , with this involution , M ...
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