## 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 2160

It will next be

) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that * ( x - y )

= 0 for every linear functional 3 * which vanishes on ( 101 – T ) X . If x * is such a ...

It will next be

**shown**that the vector x - y is in the closure of the manifold ( No I – T) X . To see this it will , in view of Corollary II . 3 . 13 , suffice to show that * ( x - y )

= 0 for every linear functional 3 * which vanishes on ( 101 – T ) X . If x * is such a ...

Page 2226

... bounded Boolean algebra of projections on X , then X has an equivalent norm

such that the functionals given by Lemma 3 . 12 can be expressed by means of a

semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ) has

... bounded Boolean algebra of projections on X , then X has an equivalent norm

such that the functionals given by Lemma 3 . 12 can be expressed by means of a

semi - inner product . On the other hand , Walsh [ 2 ; p . 315 ) has

**shown**that in ...Page 2266

It will be

multiplicity on B , Lemma 2 permits us to restrict our attention to C . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to C if and only if it is the

carrier ...

It will be

**shown**that C is a dense o - ideal in B and thus , in defining themultiplicity on B , Lemma 2 permits us to restrict our attention to C . 5 LEMMA .

The set 6 is a dense o - ideal in B . A projection belongs to C if and only if it is the

carrier ...

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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