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 40
Page 1973
... polynomial P , ( T ) in П and that any polynomial P , with the properties P ( x ) = 0 , 0 ≤ v < Vk P ( A ) = 1 , P ( A ) = 0 , k #j , 0 < v < vj , where the numbers v are arbitrary integers with v≥m , k = 1 , ... , i , will have the ...
... polynomial P , ( T ) in П and that any polynomial P , with the properties P ( x ) = 0 , 0 ≤ v < Vk P ( A ) = 1 , P ( A ) = 0 , k #j , 0 < v < vj , where the numbers v are arbitrary integers with v≥m , k = 1 , ... , i , will have the ...
Page 1985
... polynomial in 81 , ... , S. It is clear that convergence m → 9 in Ø is equivalent to the assertion that for every pair P , Q of polynomials in N variables we have ( 3 ) მ P ( 3 ) Q ( ~~ ) 9 ( 4 ) → P { ( 4 ) Q ( 2 ) 9 ( 4 ) , Pm ( s ) ...
... polynomial in 81 , ... , S. It is clear that convergence m → 9 in Ø is equivalent to the assertion that for every pair P , Q of polynomials in N variables we have ( 3 ) მ P ( 3 ) Q ( ~~ ) 9 ( 4 ) → P { ( 4 ) Q ( 2 ) 9 ( 4 ) , Pm ( s ) ...
Page 2006
... polynomial is λ — Â11 ( 8 ) whereas , for s in S2 , § ( s ) = Â ( s ) and , for such s , Ŝ ( s ) has two distinct roots . Hence for every s in the minimal polynomial of the matrix $ ( s ) has only simple roots . It remains to be shown ...
... polynomial is λ — Â11 ( 8 ) whereas , for s in S2 , § ( s ) = Â ( s ) and , for such s , Ŝ ( s ) has two distinct roots . Hence for every s in the minimal polynomial of the matrix $ ( s ) has only simple roots . It remains to be shown ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra 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 denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero