## 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 2130

K = { x € V10 x } is called the

K = { x € V10 x } is called the

**positive**cone of V ( with respect to S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK ĒK for all 1 e R , 120 , and ( iii ) Kn ( -K ) = { 0 } . Conversely , if K is a subset of V ...Page 2500

... and where K ( a ) is

... and where K ( a ) is

**positive**for almost all d if H , -H , is a**positive**operator , or more generally if there exists a Hermitian operator T , with finite range such that H , - H1 + T , is**positive**. Similar results are proved by ...Page 2564

Quasi -

Quasi -

**positive**operators . Pacific J. Math . 14 , 1029–1037 ( 1964 ) . Sawashima , I. ( see also Niiro , F. ) 1. Some counter examples in the theory of**positive**operators . Sci . Papers College Gen. Ed . Univ .### 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 countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function 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