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 2197
... indices a such that Ea11 = z1 and Eox - y ≤ ε . If a ≥ a1 , i = 1 , ... , n , then Ey = y . Thus , since E , E。= Ea it follows that , for a α , α , - | Eαx — E。x ≤ | E ̧x − y | + | y — E。x | -- αι = | E 。( E 。 x − y ) | + │y ...
... indices a such that Ea11 = z1 and Eox - y ≤ ε . If a ≥ a1 , i = 1 , ... , n , then Ey = y . Thus , since E , E。= Ea it follows that , for a α , α , - | Eαx — E。x ≤ | E ̧x − y | + | y — E。x | -- αι = | E 。( E 。 x − y ) | + │y ...
Page 2307
... indices of 7 both be equal to an integer m . Let A , i = 1 , ... , m , be a set of m linearly independent boundary values for 7. Let S be the unbounded operator in L2 ( 1 ) derived from 7 by imposition of the boundary conditions A ( f ) ...
... indices of 7 both be equal to an integer m . Let A , i = 1 , ... , m , be a set of m linearly independent boundary values for 7. Let S be the unbounded operator in L2 ( 1 ) derived from 7 by imposition of the boundary conditions A ( f ) ...
Page 2552
... indices and the spectrum of certain linear operators . Akad . Nauk Armjan . SSR Dokl . 34 , 49-55 ( 1962 ) . ( Russian . Armenian summary ) Math . Rev. 27 # 6126 , 1170 ( 1964 ) . 2 . On the invariance of the spectrum of small ...
... indices and the spectrum of certain linear operators . Akad . Nauk Armjan . SSR Dokl . 34 , 49-55 ( 1962 ) . ( Russian . Armenian summary ) Math . Rev. 27 # 6126 , 1170 ( 1964 ) . 2 . On the invariance of the spectrum of small ...
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