## 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 2162

Thus , in view of

Thus , in view of

**Theorem**4.5 , to prove the present**theorem**it suffices to show that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if the points regular relative to T are dense on to .Page 2248

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**THEOREM**. Let T be a spectral operator , and E its resolution of identity . Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p , includes a neighborhood of o ( T ) and ...Page 2283

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**THEOREM**. Let B be a complete Boolean algebra of projections in a Banach space X and let B * be the Boolean algebra of adjoints in B * . Then a projection E in B has finite uniform multiplicity n if and only if its adjoint E * in B ...### 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