## 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 1993

This is clear if á is the characteristic function of a set in and , since linear combinations of such functions are

This is clear if á is the characteristic function of a set in and , since linear combinations of such functions are

**dense**in â , it holds for all â in Â . Thus in view of ( 26 ) the equation ( 24 ) may also be written as + ( * * q ) = 1 ...Page 2156

are both

are both

**dense**in X. Since M , is**dense**in X , the manifold ( ^ , I – T ) NM , + { x | ( 9,1 – T ) ^ x = 0 } is**dense**in X , so that ( 141 – T ) ^ ( 121 – T ) * x + { x | ( 1,1 – T ) Nx = 0 } + { x | ( 121 – T ) Nx = 0 } is also**dense**...Page 2183

On the other hand , since PB contains all the elements of A ( B ) which have the form ( ii ) , and since this set of elements is

On the other hand , since PB contains all the elements of A ( B ) which have the form ( ii ) , and since this set of elements is

**dense**in A ( B ) , it will be seen that PA ( T ) = A ( B ) . Moreover , it is clear that ( I – P ) B = R ...### 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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### 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