## 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 1932

Throughout the rest of this section , x ( $ ) will denote such a maximal extension of R ( ; T ' ) . in all cases when R ( $ ; T ' ) x has the single

Throughout the rest of this section , x ( $ ) will denote such a maximal extension of R ( ; T ' ) . in all cases when R ( $ ; T ' ) x has the single

**valued**extension property . In this case x ( $ ) is a single**valued**analytic function ...Page 1990

for some E - measurable and essentially bounded complex

for some E - measurable and essentially bounded complex

**valued**function â on RN . Before illustrating the results of the preceding section , we shall examine the structure of these operators in A and in particular show that many of the ...Page 2092

The single

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 ...### 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 defined Definition denote dense determined differential operator discrete 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