## 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 1938

N and an operator S which is of scalar type in accordance with the following

definition . + 1 DEFINITION . A

case it is a spectral operator which satisfies the equation S = f AE ( da ) , where E

is ...

N and an operator S which is of scalar type in accordance with the following

definition . + 1 DEFINITION . A

**bounded operator**S is said to be of scalar type incase it is a spectral operator which satisfies the equation S = f AE ( da ) , where E

is ...

Page 2169

Spectral Theory : Self Adjoint

Theodore Schwartz. uniform limit ... LEO ( T ) These facts show that the

Elo ) defined by ( iv ) is a

Spectral Theory : Self Adjoint

**Operators**in Hilbert Space Nelson Dunford, JacobTheodore Schwartz. uniform limit ... LEO ( T ) These facts show that the

**operator**Elo ) defined by ( iv ) is a

**bounded**spectral measure which , in view of the Orlicz ...Page 2239

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

**bounded operator**. If x is in E ( 7 ) X as well as in E ( e ) X , it follows from the ...### What people are saying - Write a review

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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