## Linear Operators: Spectral operators |

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Page 2172

in lm to be the element y — (ijj, 7j2 > • • □)» where Let J7 be the Unear manifold

in (£„)* spanned by the coordinate ... E. 9 (Fixman) Let T, E, and A be as in the

preceding exercise and

) ...

in lm to be the element y — (ijj, 7j2 > • • □)» where Let J7 be the Unear manifold

in (£„)* spanned by the coordinate ... E. 9 (Fixman) Let T, E, and A be as in the

preceding exercise and

**let F**be defined for each Borel set a by F(a) =E(a) + AE(a) ...

Page 2242

T = T(f) in the sense of Definition 10, where /(z) = z, then T is said to be an

unbounded spectral operator of scalar type. The projection valued measure E is

... x in Let e be a given Borel set, and A £ e.

0 for z ...

T = T(f) in the sense of Definition 10, where /(z) = z, then T is said to be an

unbounded spectral operator of scalar type. The projection valued measure E is

... x in Let e be a given Borel set, and A £ e.

**Let f**(z) = (A — z) ' 1 for zee and/ (2) =0 for z ...

Page 2244

Let S be a set, 2 a o-field of subsets of S, and E a strongly countably additive

resolution of the identity defined on 27.

on S. Then the operator T(f) of Definition 10 is a scalar type spectral operator,

whose ...

Let S be a set, 2 a o-field of subsets of S, and E a strongly countably additive

resolution of the identity defined on 27.

**Let f**be a E-measurable function definedon S. Then the operator T(f) of Definition 10 is a scalar type spectral operator,

whose ...

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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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