Linear Operators: Spectral operators |
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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 , έe D ( f ) . έ = p ( T ) . 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 , έe D ( f ) . έ = p ( T ) . 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 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero