Linear Operators: Spectral theory |
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Page 889
As will be seen in the next section , a normal operator T in Hilbert space H
determines a spectral measure which is defined on the Boolean algebra B of all
Borel sets in the plane and which satisfies ( iv ) for every de B . This spectral
measure ...
As will be seen in the next section , a normal operator T in Hilbert space H
determines a spectral measure which is defined on the Boolean algebra B of all
Borel sets in the plane and which satisfies ( iv ) for every de B . This spectral
measure ...
Page 913
14 ) , let { en } be a sequence of Borel sets such that X = v ; ( en ) = 0 , and such
that if e is a Borel subset of the complement en of en and No v ; ( e ) = 0 , then un
( e ) = 0 . Let o be the entire complex plane , and put on = U - n ; for n 2 1 .
14 ) , let { en } be a sequence of Borel sets such that X = v ; ( en ) = 0 , and such
that if e is a Borel subset of the complement en of en and No v ; ( e ) = 0 , then un
( e ) = 0 . Let o be the entire complex plane , and put on = U - n ; for n 2 1 .
Page 1900
1 ( 41 ) Borel field of sets , definition , III . 5 . 10 20 B B - algebra . ( See Algebra )
B * - algebras , IX . 3 ( 874 – 879 ) . ( See also Algebra ) B - space ( or Banach
space ) , basic properties of , Chap . II definition , II . 3 . 2 . ( 59 ) integration , Chap
.
1 ( 41 ) Borel field of sets , definition , III . 5 . 10 20 B B - algebra . ( See Algebra )
B * - algebras , IX . 3 ( 874 – 879 ) . ( See also Algebra ) B - space ( or Banach
space ) , basic properties of , Chap . II definition , II . 3 . 2 . ( 59 ) integration , Chap
.
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero