## Linear Operators: Spectral theory |

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where o , d are arbitrary

where o , d are arbitrary

**spectral**sets and where is the void set . Here we have used the notations AB and A v B for the intersection and union of two commuting projections A and B. We recall that these operators are defined by the ...Page 933

The

The

**spectral**sets of von Neumann . If T is a bounded linear operator in a Hilbert space , then von Neumann [ 3 ] defines a closed set S of the complex sphere to be a**spectral**set of T if / ( T ) exists and ( T ) 31 whenever f is a ...### 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