## 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 2066

Since tft is a

Since tft is a

**continuous**map of RN into L. ( XI.3.1 ( f ) ) and since h is**continuous**( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is**continuous**in t . Since fs * f1 = f8 ++ * f we have h ( fs ) h ( fr ) = h ( fs + t ) h ( f ) ...Page 2443

Let g ( x , y ) be defined and

Let g ( x , y ) be defined and

**continuous**on the triangle D = { [ x , y ] 0 Sys a $ 1 } , and let G be the integral operator ( of “ Volterra type ” ) defined by ( 2 ) ( Cf ) ( x ) = * 9 ( x , y ) f ( y ) dy , fe Lp [ 0 , 1 ] .Page 2448

... discrete and

... discrete and

**continuous**spectrum . In the present section we shall illustrate this assertion by proving a number of results , due to Robert E. L. Turner , concerning the spectral character of certain classes of compact operators .### 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