## Linear Operators: Spectral operators |

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Page 2147

Conversely , let the bounded

Conversely , let the bounded

**linear operator**T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( S ( T ) , ** ) with a resolution of the identity which is countably ...Page 2162

If the bounded

If the bounded

**linear operator**T in a weakly complete space has properties ( B ) and ( G ) then , by Lemma 4 , it has properties ( A ) and ( C ) . Thus , in view of Theorem 4.5 , to prove the present theorem it suffices to show that T ...Page 2400

Friedrichs ' Method of Similar Operators In the present section we shall begin our discussion of an elegant method ... Let X be a B - space , and let T be a

Friedrichs ' Method of Similar Operators In the present section we shall begin our discussion of an elegant method ... Let X be a B - space , and let T be a

**linear operator**in X ; let K be a second**linear operator**in X which is , in a ...### 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