Linear Operators: Spectral operators |
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Page 2113
... Foiaş [ 12 ] and Colojoară and Foias [ 1 , 4 ] . See also Apostol [ 4 , 5 , 11 , 15 ] , Colojoară and Foias [ 2 , 5 ] , Kariotis [ 1 ] , and Vasilescu [ 3 , 4 , 5 , 6 , 7 , 8 ] for other results concerning decomposable operators . n Let ...
... Foiaş [ 12 ] and Colojoară and Foias [ 1 , 4 ] . See also Apostol [ 4 , 5 , 11 , 15 ] , Colojoară and Foias [ 2 , 5 ] , Kariotis [ 1 ] , and Vasilescu [ 3 , 4 , 5 , 6 , 7 , 8 ] for other results concerning decomposable operators . n Let ...
Page 2118
... Foias [ 11 ] , or Colojoară and Foias [ 4 ] ) . For examples of generalized scalar operators that are not spectral operators , let X = C ' [ 0 , 1 ] , ( r = 0 , 1 , 2 , . . . ) with norm | ƒ | = - sup { | f ( t ) | , | ƒ ' ( t ) ...
... Foias [ 11 ] , or Colojoară and Foias [ 4 ] ) . For examples of generalized scalar operators that are not spectral operators , let X = C ' [ 0 , 1 ] , ( r = 0 , 1 , 2 , . . . ) with norm | ƒ | = - sup { | f ( t ) | , | ƒ ' ( t ) ...
Page 2129
... Foias [ 1 , 6 , 9 , 10 ] , Volk [ 1 ] , Wermer [ 1 , 2 , 4 ] . Contractions and dilations . On pages 931-932 we have briefly discussed contractions and dilations of operators in Hilbert space . This theory , which was sparked by some ...
... Foias [ 1 , 6 , 9 , 10 ] , Volk [ 1 ] , Wermer [ 1 , 2 , 4 ] . Contractions and dilations . On pages 931-932 we have briefly discussed contractions and dilations of operators in Hilbert space . This theory , which was sparked by some ...
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