## 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

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

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

respect to S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK S K for all de

R ...

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

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

**positive**cone of V ( withrespect to S ) ; it is easy to see that K satisfies ( i ) K + K SK , ( ii ) AK S K for all de

R ...

Page 2564

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 -

...

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...

Page 2565

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

Theodore Schwartz. Eine Bemerkung zur Existenz invarianter Teilräume linearer

Abbildungen . Math . Zeit . 82 , 90 ( 1963 ) . On the point spectrum of

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

Theodore Schwartz. Eine Bemerkung zur Existenz invarianter Teilräume linearer

Abbildungen . Math . Zeit . 82 , 90 ( 1963 ) . On the point spectrum of

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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