## Linear Operators: Spectral theory |

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Page 1262

28 Let a self adjoint operator A in a

there exists a

that Ax = PQx , XEH , P denoting the orthogonal projection of Hi on H . 29 Let { Tn

} ...

28 Let a self adjoint operator A in a

**Hilbert space**H with O SA SI be given . Thenthere exists a

**Hilbert space**H , 2H , and an orthogonal projection Q in H , suchthat Ax = PQx , XEH , P denoting the orthogonal projection of Hi on H . 29 Let { Tn

} ...

Page 1774

Of the infinite dimensional B-spaces,

especially in its elementary geometrical aspects, to the Euclidean or finite

dimensional unitary spaces. It is not immediate from the definition that a

Of the infinite dimensional B-spaces,

**Hilbert space**is the most closely related,especially in its elementary geometrical aspects, to the Euclidean or finite

dimensional unitary spaces. It is not immediate from the definition that a

**Hilbert****space**is a ...Page 1773

APPENDIX

numbers , together with a complex function ( : , : ) defined on HXH with the

following properties : ( i ) ( x , x ) = 0 if and only if x = 0 ; ( ii ) ( c , c ) 2 0 , 2 c ; ( iii ) (

x + y , z ) ...

APPENDIX

**Hilbert space**is a linear vector space H over the field of complexnumbers , together with a complex function ( : , : ) defined on HXH with the

following properties : ( i ) ( x , x ) = 0 if and only if x = 0 ; ( ii ) ( c , c ) 2 0 , 2 c ; ( iii ) (

x + y , z ) ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

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### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero