## 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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Results 1-3 of 91

Page 1990

for some E - measurable and essentially bounded complex valued function â on

RN . ... ( s ) = 1 968 – t ) u ( dt ) , QEH , determined by a complex valued function f

on RN or a complex valued

for some E - measurable and essentially bounded complex valued function â on

RN . ... ( s ) = 1 968 – t ) u ( dt ) , QEH , determined by a complex valued function f

on RN or a complex valued

**set function**, defined on a family E ( a ) of sets in RN .Page 1993

in û may be written in terms of the measure u of equation ( 16 ) as ( 26 ) âp = a ( s

) u ( ds ) o , QEH . This is clear if á is the characteristic

since linear combinations of such

in û may be written in terms of the measure u of equation ( 16 ) as ( 26 ) âp = a ( s

) u ( ds ) o , QEH . This is clear if á is the characteristic

**function**of a**set**in Eand ,since linear combinations of such

**functions**are dense in â , it holds for all â in .Page 2029

It is clear that it T , U are in T ( RN ) and a , ß are constants , then the function aT +

BU defined on by ( i ) ( aT + BU ) ( Q ) ... determined by a bounded finitely additive

...

It is clear that it T , U are in T ( RN ) and a , ß are constants , then the function aT +

BU defined on by ( i ) ( aT + BU ) ( Q ) ... determined by a bounded finitely additive

**set function**v ( defined on some field of sets in RN which includes the open sets )...

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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