## Linear Operators: Spectral operators |

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Page 1948

The sum and the product of two

space are also spectral operators . The proof of this corollary will use the

following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space

with A ...

The sum and the product of two

**commuting**bounded spectral operators in Hilbertspace are also spectral operators . The proof of this corollary will use the

following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space

with A ...

Page 2098

See also Deal [ 2 ] . The following result was proved by Sine [ 1 ] , using

techniques similar to those in Smart [ 2 ] . Let T e B ( X ) with o ( T ) = o ( T ) $ [ 0 ,

1 ] with a bounded

projections ...

See also Deal [ 2 ] . The following result was proved by Sine [ 1 ] , using

techniques similar to those in Smart [ 2 ] . Let T e B ( X ) with o ( T ) = o ( T ) $ [ 0 ,

1 ] with a bounded

**commuting**strongly continuous family E ( t ) , te [ 0 , 1 ] , ofprojections ...

Page 2177

Introduction The sum and product of two

in Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen

that this principle could be extended to the sum and product of two

Introduction The sum and product of two

**commuting**bounded normal operatorsin Hilbert space is normal and hence spectral . In Corollary XV . 6 . 5 it was seen

that this principle could be extended to the sum and product of two

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniform uniformly unique valued vector weakly zero