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 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 ...
... 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 ...
Page 1990
... valued function f on RN or a complex valued set function defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is , whether ...
... valued function f on RN or a complex valued set function defined on a family ( A ) of sets in RN . The representation ( 18 ) or ( 19 ) of a given convolution operator depends upon the interpreta- tion of the integral , that is , whether ...
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 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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 invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian 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