## Linear Operators: Spectral operators |

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Page 1936

The unique countably additive resolution of the

in the plane which is determined by a spectral operator T is called the resolution

of the

...

The unique countably additive resolution of the

**identity**defined on the Borel setsin the plane which is determined by a spectral operator T is called the resolution

of the

**identity**for T. 10 Theorem. Let I =S1-\ h En where Ex, . . . , En are bounded,...

Page 2094

12) that if J is a weakly complete B-space, then any prespectral operator is

automatically spectral, and so has a unique resolution of the

and Dowson [1] have considered prespectral operators in some detail and have

obtained ...

12) that if J is a weakly complete B-space, then any prespectral operator is

automatically spectral, and so has a unique resolution of the

**identity**. Berksonand Dowson [1] have considered prespectral operators in some detail and have

obtained ...

Page 2242

The projection valued measure E is said to be the resolution of the

13 Lemma. An unbounded spectral operator of scalar type in the sense of

Definition 12 is a spectral operator in the sense of Definition 1. Moreover, the

resolution ...

The projection valued measure E is said to be the resolution of the

**identity**for T.13 Lemma. An unbounded spectral operator of scalar type in the sense of

Definition 12 is a spectral operator in the sense of Definition 1. Moreover, the

resolution ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane 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 uniformly unique valued vector weakly zero