## Linear Operators: Spectral operators |

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Results 1-3 of 71

Page 1936

Let I = E + + En where E1 , ... , En are bounded , disjoint projections in X , each

commuting with the bounded operator T. Then T is a spectral operator if and only

if each

Let I = E + + En where E1 , ... , En are bounded , disjoint projections in X , each

commuting with the bounded operator T. Then T is a spectral operator if and only

if each

**restriction**T | E ; X is a spectral operator . If T is a spectral operator , then ...Page 2094

X ) is reduced by a closed subspace Y SX and one of its complements ( that is , if

T commutes with some projection of X onto Y ) , then the

**Restrictions**and quotients . Theorem 3.10 shows that if a spectral operator Te B (X ) is reduced by a closed subspace Y SX and one of its complements ( that is , if

T commutes with some projection of X onto Y ) , then the

**restriction**T Y of T to Y ...Page 2228

If o is a Borel set , and T is a spectral operator with resolution of the identity E ,

then the

resolution of the identity is the

) X is ...

If o is a Borel set , and T is a spectral operator with resolution of the identity E ,

then the

**restriction**T | E ( 0 ) X of T to E ( 0 ) X is a spectral operator whoseresolution of the identity is the

**restriction**of E to E ( o ) X . If o is bounded , T | E ( 0) X is ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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