## 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 1990

This elementary observation suggests that it might be easier to give certain convolutions an integral representation if we use the integral of

This elementary observation suggests that it might be easier to give certain convolutions an integral representation if we use the integral of

**vector**valued functions , and this we shall do . We begin by defining the convolution ...Page 2160

It will next be shown that the

It will next be shown that the

**vector**x y is in the closure of the manifold ( 1.1 – T ) X . To see this it will , in view of Corollary II.3.13 , suffice to show that ** ( 2 — y ) = 0 for every linear functional 3 * which ...Page 2279

26 THEOREM . Let N be an X - closed invariant subspace in X * and let x * be a functional whose carrier is in 6 * . If Nn N ( ** ) = ( 0 ) , then there exists a

26 THEOREM . Let N be an X - closed invariant subspace in X * and let x * be a functional whose carrier is in 6 * . If Nn N ( ** ) = ( 0 ) , then there exists a

**vector**xo € X such that ( 1 ) y * ( x . ) ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

31 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 contained continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear 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