## Linear operators: Spectral operators |

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Results 1-3 of 77

Page 1953

First

in X* with x* =£ 0 and x*TX = 0. Let a^ ^ 0 and define the operator .4 by the

equation Ax = a;*(a;)a;1, so that A ?t 0. But .4T = 0, which contradicts Corollary 11

.

First

**suppose**that A = 0. If TX is not dense then, by Corollary II.3.13, there is an x*in X* with x* =£ 0 and x*TX = 0. Let a^ ^ 0 and define the operator .4 by the

equation Ax = a;*(a;)a;1, so that A ?t 0. But .4T = 0, which contradicts Corollary 11

.

Page 2284

However, rather than seek the maximum generality, it will be convenient to

these properties hold for B if X is separable, so this will be assumed for the rest of

this ...

However, rather than seek the maximum generality, it will be convenient to

**suppose**that B is itself complete and satisfies the countable chain condition. Boththese properties hold for B if X is separable, so this will be assumed for the rest of

this ...

Page 2303

enumeration of its spectrum. Let d„ denote the distance from An to o{T) — {An}.

**Suppose**that E is its resolution of the identity, and**suppose**that {X„} is anenumeration of its spectrum. Let d„ denote the distance from An to o{T) — {An}.

**Suppose**that for all but a finite number of n, E(Xn) has a one- dimensional range.### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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