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 2113
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace Y of a B - space X to be a spectral maximal subspace of Te B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
... subspace may have spectrum larger than o ( T ) . Foias [ 12 ] defined a closed linear subspace Y of a B - space X to be a spectral maximal subspace of Te B ( X ) if ( i ) Y is invariant under T , and ( ii ) if 3 is a closed linear subspace ...
Page 2114
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if σ is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then E. is a spectral maximal subspace of T. Hence both ...
... subspace E ( F ) X is a spectral maximal subspace for T. Similarly if σ is a spectral set ( in the sense of VII.3.17 ) and if E , is the corresponding projection operator , then E. is a spectral maximal subspace of T. Hence both ...
Page 2286
... subspace in X , we denote by P ( M ) the closure in H of the linear set A ( M ~ D ( A ) ) . Similarly if K is a closed invariant subspace in H , Y ( K ) denotes the closure in X of A - 1 ( RD ( A - 1 ) ) . It follows from Theorem 19 ( b ) ...
... subspace in X , we denote by P ( M ) the closure in H of the linear set A ( M ~ D ( A ) ) . Similarly if K is a closed invariant subspace in H , Y ( K ) denotes the closure in X of A - 1 ( RD ( A - 1 ) ) . It follows from Theorem 19 ( b ) ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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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