Linear Operators, Part 2 |
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Results 1-3 of 86
Page 2134
... sufficient for a bounded operator T to be a spectral operator . The conditions given will be expressed in terms of the resolvent R ( § ; T ) and the analytic extensions x ( ) of R ( § ; T ) x . We have already established a number of ...
... sufficient for a bounded operator T to be a spectral operator . The conditions given will be expressed in terms of the resolvent R ( § ; T ) and the analytic extensions x ( ) of R ( § ; T ) x . We have already established a number of ...
Page 2179
... sufficiently large n , and A1 → A - 1 uniformly . To A1 show that A - 1 is in ( B ) it is consequently sufficient to show that A1 is in A ( B ) . Thus we may suppose without loss of generality that A is in Ao ( B ) , that is , that A ...
... sufficiently large n , and A1 → A - 1 uniformly . To A1 show that A - 1 is in ( B ) it is consequently sufficient to show that A1 is in A ( B ) . Thus we may suppose without loss of generality that A is in Ao ( B ) , that is , that A ...
Page 2290
... sufficient to insure that it is a spectral operator . The basic idea of the method is the following : if T is spectral , and if P is , in some suitable sense , sufficiently small relative to T , then T + P will also be spectral . It ...
... sufficient to insure that it is a spectral operator . The basic idea of the method is the following : if T is spectral , and if P is , in some suitable sense , sufficiently small relative to T , then T + P will also be spectral . It ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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