## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2130

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 x } is called the

to S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK ĒK for all 1 e R ...

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. K = { x € V10 x } is called the

**positive**cone of V ( with respectto S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK ĒK for all 1 e R ...

Page 2500

... and where K ( a ) is

more generally if there exists a Hermitian operator T , with finite range such that H

, - H1 + T , is

... and where K ( a ) is

**positive**for almost all d if H , -H , is a**positive**operator , ormore generally if there exists a Hermitian operator T , with finite range such that H

, - H1 + T , is

**positive**. Similar results are proved by Birman and Krein for a pair ...Page 2564

2 . A remark on the Volterra operator . J. Math . Anal . Appl . 12 , 244–246 ( 1965 )

. 3. Invariant subspaces and unstarred operator algebras . Pacific J. Math . 17 ,

511-517 ( 1966 ) . Sasser , D. W. 1. Quasi -

2 . A remark on the Volterra operator . J. Math . Anal . Appl . 12 , 244–246 ( 1965 )

. 3. Invariant subspaces and unstarred operator algebras . Pacific J. Math . 17 ,

511-517 ( 1966 ) . Sasser , D. W. 1. Quasi -

**positive**operators . Pacific J. Math .### 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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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 discrete 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