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 81
Page 1951
... linear subspace of X , then the set of bounded linear operators A in X for which AX ≤ is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ...
... linear subspace of X , then the set of bounded linear operators A in X for which AX ≤ is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ...
Page 1960
... linear map A : x → y of HP into itself , it is easy to define a set a , of p2 bounded linear maps in 5 such that the equation y = Ax is equivalent to the system ( 4 ) . To see this , let A be a bounded linear map in 5o and let 5 , be ...
... linear map A : x → y of HP into itself , it is easy to define a set a , of p2 bounded linear maps in 5 such that the equation y = Ax is equivalent to the system ( 4 ) . To see this , let A be a bounded linear map in 5o and let 5 , be ...
Page 2400
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
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