Linear Operators: Spectral operators |
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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 - TXE ( X ) , E ( 8 ) ...
... 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 - TXE ( X ) , E ( 8 ) ...
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 2193
... arbitrary B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then ...
... arbitrary B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero