## 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 2122

Analogously , Smart [ 2 ] defined an operator T to be well - bounded if there exists a constant K > 0 such that | p ( T ) S K || P || , whence ||

Analogously , Smart [ 2 ] defined an operator T to be well - bounded if there exists a constant K > 0 such that | p ( T ) S K || P || , whence ||

**denotes**the norm on the space BV [ 0 , 1 ] ( i.e. , || P || = | P ( 0+ ) | + v ( p ...Page 2136

Definition XV.2.6 ) that the resolvent set of x , which is

Definition XV.2.6 ) that the resolvent set of x , which is

**denoted**by p ( x ) , may be defined as the union of all the domains D ( f ) , the union being taken as f varies over all analytic extensions of R ( $ ; T ) x .Page 2442

( b ) The operator S = Z , TZ , 1 has the domain ( 48 ) DIS ) = { se L. || * 8 * 15 ( p l2 dp < 00 ] and satisfies ( 49 ) ( Sf ) ( o ) = pf ( p ) , fe D ( S ) . ( c ) If V ,

( b ) The operator S = Z , TZ , 1 has the domain ( 48 ) DIS ) = { se L. || * 8 * 15 ( p l2 dp < 00 ] and satisfies ( 49 ) ( Sf ) ( o ) = pf ( p ) , fe D ( S ) . ( c ) If V ,

**denotes**the operator in L2 ( E ) defined by ( 50 ) ( V1f ) ( x ) ...### 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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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