## Linear Operators: Spectral theory |

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Page 888

Here we have used the notations A , B and A v B for the intersection and union of

two commuting

union of two commuting

Here we have used the notations A , B and A v B for the intersection and union of

two commuting

**projections**A and B. We ... Also the ranges of the intersection andunion of two commuting

**projection**operators are given by the equations ( A i B ) ...Page 1123

We say that E is a subdiagonalizing

invariant , i.e. , if ET E = TE . 3 LEMMA . Any operator T in Hilbert space admits a

maximal totally ordered set F of orthogonal subdiagonalizing

...

We say that E is a subdiagonalizing

**projection**for T if T leaves the range of Einvariant , i.e. , if ET E = TE . 3 LEMMA . Any operator T in Hilbert space admits a

maximal totally ordered set F of orthogonal subdiagonalizing

**projections**; i.e. , a...

Page 1126

Since each

function of T is a strong limit of linear combinations of the

from ( 1 ) that the closure in H ( am ) of the vectors ( 4 ) is H ( Xm ) . Thus , by ...

Since each

**projection**in the spectral resolution of T and hence each continuousfunction of T is a strong limit of linear combinations of the

**projections**Ei , it followsfrom ( 1 ) that the closure in H ( am ) of the vectors ( 4 ) is H ( Xm ) . Thus , by ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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