## Linear Operators: Spectral theory |

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Page 888

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

two commuting

and union of two commuting

B ) ...

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

two commuting

**projections**A and B . We ... Also the ranges of the intersectionand union of two commuting

**projection**operators are given by the equations ( A iB ) ...

Page 1123

We say that E is a subdiagonalizing

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

maximal totally ordered set F of orthogonal subdiagonalizing

a ...

We say that E is a subdiagonalizing

**projection**for T if T leaves the range of Einvariant , i . e . , if ETE = 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 ( xm ) 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 ( xm ) of the vectors ( 4 ) is H ( xm ) . Thus , by ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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