## 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 2146

It will first be

It will first be

**shown**that EI – T is one - to - one on E ( S ) X . If € x is in E ( 8 ) X and ( EI - T ' ) . C = 0 , then , since ( T - E1 ) " R ( ^ ; T ) = Σ n = o ( – É ) n + 1 ! for all large 1 , it is seen that w ( a ) = x / ( 1 ...Page 2160

It will next be

It will next be

**shown**that the vector x y is in the closure of the manifold ( 1.1 – T ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that w * ( x - y ) = 0 for every linear functional x * which vanishes on ...Page 2226

315 ) has

315 ) has

**shown**that in a complete metrizable locally convex space there may not be a single functional corresponding to x * ; however , some of the results presented here can still be generalized . Walsh [ 1 ] showed that if A is a ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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