## Linear Operators: Spectral theory |

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Page 906

... symmetric or Hermitian if T = T * ;

... symmetric or Hermitian if T = T * ;

**positive**if it is self adjoint and if ( Tr , x ) 20 for every x in y ; and**positive**definite if it is**positive**and ...Page 1247

Q.E.D. Next we shall require some information on

Q.E.D. Next we shall require some information on

**positive**self adjoint transformations and their square roots . 2 LEMMA . A self adjoint transformation T is ...Page 1338

Let { M is } be a

Let { M is } be a

**positive**matrix measure whose elements Mis are continuous with respect to a**positive**o - finite measure u . If the matrix of densities ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 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 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