## 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 1931

If x is a vector in X , then by an analytic

If x is a vector in X , then by an analytic

**extension**of R ( É ; T ' ) x will be meant an X - valued function f defined and analytic on an open set D ( S ) 2 p ( T ) and such that ( ŠI – T ) f ( $ ) = x , & € D ( f ) .Page 2092

The single valued

The single valued

**extension**property . The example of an operator which does not have the single valued**extension**property that is given in Section 2 is due to S. Kakutani ( see Dunford [ 18 ] ) . Kesel'man ( 1 ) gave necessary ...Page 2095

Although the restrictions of operators with the single valued

Although the restrictions of operators with the single valued

**extension**property have this property ( see Dowson [ 1 ] ) , the corresponding result for quotients is not true . Indeed , Dowson [ 3 ] notes that the unitary shift operator ...### 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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### 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 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