## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2094

Theorem 3.10 shows that if a spectral operator Te B ( X ) is reduced by a closed

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 is spectral .Page 2113

Thus the restriction of an operator T to an arbitrary invariant closed

Thus the restriction of an operator T to an arbitrary invariant closed

**subspace**may have spectrum larger than o ( T ) . Foiaş [ 12 ] defined a closed linear**subspace**y of a B - space X to be a spectral maximal**subspace**of Te B ( X ) if ...Page 2114

It is not difficult to see that if T is a spectral operator with resolution of the identity E , then for F closed in o ( T ) , the

It is not difficult to see that if T is a spectral operator with resolution of the identity E , then for F closed in o ( T ) , the

**subspace**E ( F ) X is a spectral maximal**subspace**for T. Similarly if o is a spectral set in the sense of ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero