Linear Operators: Spectral operators |
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Page 1932
... valued extension property . In this case x ( ) is a single valued analytic function with domain p ( x ) and with x ( ) = R ( ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ...
... valued extension property . In this case x ( ) is a single valued analytic function with domain p ( x ) and with x ( ) = R ( ; T ) x , ξερ ( Τ ) . It will be shown in the next section that , if T is a spectral operator , the function R ...
Page 1990
... valued function â on RN . Before illustrating the results of the preceding section , we shall examine the structure ... valued function ƒ on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The ...
... valued function â on RN . Before illustrating the results of the preceding section , we shall examine the structure ... valued function ƒ on RN or a complex valued set function à defined on a family ( A ) of sets in RN . The ...
Page 2092
... valued 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 ...
... valued 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 ...
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