## Linear Operators: Spectral operators |

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Page 2169

This shows that ( vi ) holds for every

continuous function g . A repetition of this argument shows that it also holds if f

and g are both

commute and ...

This shows that ( vi ) holds for every

**bounded**Borel function f and everycontinuous function g . A repetition of this argument shows that it also holds if f

and g are both

**bounded**Borel functions . Thus the**operators**f ( T ) and g ( T )commute and ...

Page 2239

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Since f Xe

is a bounded function , the operator T ' ( f Xe ) is a

ē ) X as well as in E ( e ) X , it follows from the operational calculus for bounded ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. Since f Xe

is a bounded function , the operator T ' ( f Xe ) is a

**bounded operator**. If x is in E (ē ) X as well as in E ( e ) X , it follows from the operational calculus for bounded ...

Page 2252

An attempt to follow the development in the

runs into difficulties . The

quasi - nilpotent restriction to each space E ( o ) X with o

An attempt to follow the development in the

**bounded**case by writing N = T - Sruns into difficulties . The

**operator**N , although easily seen by Lemma 2 to have aquasi - nilpotent restriction to each space E ( o ) X with o

**bounded**, need not be ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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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