Linear Operators, Part 2 |
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Page 1938
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Nelson Dunford, Jacob T. Schwartz. N and an operator S which is of scalar type in accordance with the follow- ing definition . 1 DEFINITION . A bounded operator S is said to be of scalar type in case it is a spectral operator which ...
Page 2094
... spectral operator and Y is a closed subspace invariant under T , then the operator T2 ( defined on X / Y by T1 [ x ] = [ Tx ] ) is a spectral operator if and only if is invariant under the resolution of the 2094 XV.16 XV . SPECTRAL ...
... spectral operator and Y is a closed subspace invariant under T , then the operator T2 ( defined on X / Y by T1 [ x ] = [ Tx ] ) is a spectral operator if and only if is invariant under the resolution of the 2094 XV.16 XV . SPECTRAL ...
Page 2174
... operator U is not spectral . See also Krabbe [ 3 ] where it is also noted that the Hilbert trans- form on l ... type operator with real spectrum . ( This follows from Lemma XV.6.1 which ... SPECTRAL OPERATORS : SUFFICIENT CONDITIONS.
... operator U is not spectral . See also Krabbe [ 3 ] where it is also noted that the Hilbert trans- form on l ... type operator with real spectrum . ( This follows from Lemma XV.6.1 which ... SPECTRAL OPERATORS : SUFFICIENT CONDITIONS.
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 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