## Linear Operators: Spectral theory |

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Page 860

A B -

A B -

**algebra**X is commutative in case xy = yx for all x and y in X. An involution in a B -**algebra**X is a mapping x ... the exception of L ( -00,00 ) and the class of analytic functions , are commutative B -**algebras**with involutions .Page 875

The

The

**algebra**B ( ö ) of all bounded linear operators in Hilbert space H in which the operation * of involution is defined by equation ( i ) is a B ... Our chief objective in this section is to characterize commutative B * -**algebras**.Page 979

be based upon two closely related commutative

be based upon two closely related commutative

**algebras**of operators in the Hilbert space L2 ( R ) . One of these**algebras**, namely the**algebra**A of the preceding section , we have met before . For convenience , its definition and some ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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additive adjoint operator 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 satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero