## 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

Restrictions and quotients . Theorem 3 . 10 shows that if a spectral operator Te B

( X ) is reduced by a closed

if T commutes with some projection of X onto Y ) , then the restriction T | Y of T to ...

Restrictions and quotients . Theorem 3 . 10 shows that if a spectral operator Te B

( X ) is reduced by a closed

**subspace**Y = X 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 ...

Page 2113

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

may have spectrum larger than o ( T ) . Foiaş [ 12 ] defined a closed linear

Y is ...

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 ( i )Y is ...

Page 2114

17 ) and if E , is the corresponding projection operator , then E , X is a spectral

maximal

of o ( T ) there is a family Y . , . . . , Yn of spectral maximal

that ...

17 ) and if E , is the corresponding projection operator , then E , X is a spectral

maximal

**subspace**of T . Hence both ... if for every finite open cover G1 , . . . , G ,of o ( T ) there is a family Y . , . . . , Yn of spectral maximal

**subspaces**of T suchthat ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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### Common terms and phrases

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 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