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 1931
... extension of R ( § ; T ) x will be meant an X - valued function ƒ defined and analytic on an open set D ( f ) ≥ p ( T ) and such that It is clear that , for such an extension , ( §I — T ) ƒ ( § ) = x , § = D ( ƒ ) . ξερ ( Τ ) . ƒ ...
... extension of R ( § ; T ) x will be meant an X - valued function ƒ defined and analytic on an open set D ( f ) ≥ p ( T ) and such that It is clear that , for such an extension , ( §I — T ) ƒ ( § ) = x , § = D ( ƒ ) . ξερ ( Τ ) . ƒ ...
Page 2092
... extension property . The example of an operator which does not have the single valued extension property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man [ 1 ] gave necessary conditions for an operator ...
... extension property . The example of an operator which does not have the single valued extension property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man [ 1 ] gave necessary conditions for an operator ...
Page 2095
... extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed , Dowson [ 3 ] notes that the unitary shift operator has quotients which do not have the single valued extension ...
... extension property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed , Dowson [ 3 ] notes that the unitary shift operator has quotients which do not have the single valued extension ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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 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