## Linear Operators: Spectral operators |

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Page 1936

If T is a spectral operator, then the resolution of the

X is the corresponding restriction of the resolution of the

be a spectral operator. By Corollary 7. Et commutes with every projection E(o; ...

If T is a spectral operator, then the resolution of the

**identity**for the restriction T \ E,X is the corresponding restriction of the resolution of the

**identity**for T. Proof. Let Tbe a spectral operator. By Corollary 7. Et commutes with every projection E(o; ...

Page 2094

12) that if 3E 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 ...

12) that if 3E 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 ...

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 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

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