## Linear Operators: Spectral theory |

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Page 888

a where o , & are arbitrary spectral sets and where is the void set . ... This observation leads to the notion of a

a where o , & are arbitrary spectral sets and where is the void set . ... This observation leads to the notion of a

**spectral measure**in a B - space X. A**spectral measure**in X is a homomorphic map of a Boolean algebra of sets into a ...Page 889

Without relaxing the condition ( iii ) this is clearly impossible , for if 8 = o ( T ) then , since the spectrum of an operator is always closed ( IX.1.5 ) , every set in the domain of a

Without relaxing the condition ( iii ) this is clearly impossible , for if 8 = o ( T ) then , since the spectrum of an operator is always closed ( IX.1.5 ) , every set in the domain of a

**spectral measure**satisfying ( iii ) is ...Page 897

SEB f ( 2 Thus δε , geC ( 1 ) , and hence Elo no ) E ( 0 ) E ( 8 ) for every pair o , din B. Hence E is a

SEB f ( 2 Thus δε , geC ( 1 ) , and hence Elo no ) E ( 0 ) E ( 8 ) for every pair o , din B. Hence E is a

**spectral measure**and , in particular , all of the projections E ( S ) commute . It follows then from ( iii ) that the projections ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero