## 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 1931

Of course it is not

Of course it is not

**clear**to begin with that a countably additive resolution of the identity defined on the Borel sets of the plane is uniquely determined by the spectral operator T. This is the case , but until it is proved we refer to ...Page 2053

In the examples of Theorems 19 and 21 we did not appeal to the general theory , as it was

In the examples of Theorems 19 and 21 we did not appeal to the general theory , as it was

**clear**from the form of exp tÂ that T ( t ) o was differentiable for t > 0 and an arbitrary q in Hp . It is even**clear**that the nth order ...Page 2159

The union of all intervals of constancy relative to T is an open set dense in I .. PROOF . It is

The union of all intervals of constancy relative to T is an open set dense in I .. PROOF . It is

**clear**that the union of intervals of constancy is open . To see that it is dense , let y be a closed subarc of T ' , having positive length ...### 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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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