## Linear Operators: Spectral operators |

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The following

The following

**result**was proved by Sine [ 1 ] , using techniques similar to those in Smart [ 2 ] . Let Te B ( X ) with o ( T ) = 0. ( T ) = [ 0 , 1 ] with a bounded commuting strongly continuous family E ( t ) , t e [ 0 , 1 ] ...Page 2214

Q.E.D. The preceding material of the present section was largely preliminary to the following basic

Q.E.D. The preceding material of the present section was largely preliminary to the following basic

**result**of Bade , which was described in the introduction . 18 THEOREM . Let B be a bounded Boolean algebra of projections in a weakly ...Page 2291

Even though the main

Even though the main

**result**of Section 3 is greatly generalized in Section 4 , we feel that it is worth inserting the simpler case of Section 3 as a kind of preparation for the more complicated case . The question of deciding when the ...### 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 | 1929 |

Copyright | |

32 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 countably additive defined Definition denote dense determined differential operator 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