## Linear Operators: Spectral operators |

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Page 1909

The exclusion of the theory of spectral operators from Part II was not due solely to the growth of the literature in this field , but was determined also by our desire to

The exclusion of the theory of spectral operators from Part II was not due solely to the growth of the literature in this field , but was determined also by our desire to

**present**a number of important applications of the general theory ...Page 2227

The

The

**present**chapter is an attempt to make the corresponding step in the theory of spectral operators . We begin by defining a closed spectral operator and its resolution of the identity , and showing that the latter is unique .Page 2448

In the

In the

**present**section we shall illustrate this assertion by proving a number of results , due to Robert E. L. Turner , concerning the spectral character of certain classes of compact operators . We begin by generalizing Theorem 2.1 .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1931 |

Copyright | |

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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 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 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