## 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 2188

Let f be in EB ( 1 , E ) , and for every

Let f be in EB ( 1 , E ) , and for every

**Borel set**8 in the complex plane let E ( 8 ) = E ( F - 1 ( 8 ) ) . If g is the characteristic function of such a ...Page 2189

To see that S ( f ) is a scalar type operator with the stated resolution of the identity , let f be in EB ( 1 , 2 ) and , for every

To see that S ( f ) is a scalar type operator with the stated resolution of the identity , let f be in EB ( 1 , 2 ) and , for every

**Borel set**d in the plane ...Page 2233

The operator f ( T ) of Definition 8 is closed , linear , and independent of the particular sequence of

The operator f ( T ) of Definition 8 is closed , linear , and independent of the particular sequence of

**Borel sets**used to define it . ( i ) For each Borel ...### 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 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