## Linear Operators: Spectral operators |

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The situation corresponding to an

. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an

The situation corresponding to an

**invariant**closed subspace of T is not so simple. However , Fixman [ 1 ] proved that the restriction of a spectral operator T to an

**invariant**closed subspace y of X is spectral if and only if the resolution of the ...Page 2214

5 , the weakly closed operator algebra W ( B ) generated by B is the same as the

strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit

of finite linear combinations of elements of B . It follows that A leaves

5 , the weakly closed operator algebra W ( B ) generated by B is the same as the

strongly closed algebra generated by B . Thus every A in W ( B ) is the strong limit

of finite linear combinations of elements of B . It follows that A leaves

**invariant**...Page 2216

To do this , let A be an operator in Az and let Ho be a closed subspace of Hilbert

space which is

identity for T . Thus , if P is the orthogonal projection onto H . then , since E ( e )

leaves ...

To do this , let A be an operator in Az and let Ho be a closed subspace of Hilbert

space which is

**invariant**under every element E ( e ) of the resolution of theidentity for T . Thus , if P is the orthogonal projection onto H . then , since E ( e )

leaves ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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