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 1921
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and ... Operator 1933 4. The Canonical Reduction of a Spectral Operator 1937 5 . • An Operational Calculus for Bounded ...
Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and ... Operator 1933 4. The Canonical Reduction of a Spectral Operator 1937 5 . • An Operational Calculus for Bounded ...
Page 2094
... spectral operator and Y is a closed subspace invariant under T , then the operator T ( 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 T ( 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 2118
... operator T defined by ( Tf ) ( t ) = tf ( t ) , te [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) ƒ ) ( t ) = q ( t ) f ( t ) for q € Co . It is proved ( see Foiaş [ 9 ] or 2118 XV.16 XV . SPECTRAL ...
... operator T defined by ( Tf ) ( t ) = tf ( t ) , te [ 0 , 1 ] , is a generalized scalar operator with spectral distribution ( U ( q ) ƒ ) ( t ) = q ( t ) f ( t ) for q € Co . It is proved ( see Foiaş [ 9 ] or 2118 XV.16 XV . SPECTRAL ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero