## Linear Operators: Spectral operators |

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Page 1983

Since every s belongs to one of the sets Si , we havela - u - 1 SK for every pair , u

of distinct

operator of type p - 1 . Q . E . D . 14 COROLLARY . Let A be in AP and let S be a ...

Since every s belongs to one of the sets Si , we havela - u - 1 SK for every pair , u

of distinct

**eigenvalues**of Â ( s ) , and Corollary 7 shows that A is a spectraloperator of type p - 1 . Q . E . D . 14 COROLLARY . Let A be in AP and let S be a ...

Page 2131

272 ] ) that the

multiplicity one ; if this point spectrum contains an isolated point , then these

pole of ...

272 ] ) that the

**eigenvalues**on the unit circle are cyclically located and each hasmultiplicity one ; if this point spectrum contains an isolated point , then these

**eigenvalues**are the nth roots of unity for some n . If one such**eigenvalue**is apole of ...

Page 2536

On the separation of the

Mathematica ( Cluj ) 4 ( 27 ) , 253 – 260 ( 1962 ) . ( Russian ) Math . Rev . 29 #

6311 , 1182 ( 1965 ) . Theorems of comparison type for

operators ...

On the separation of the

**eigenvalues**of operators with discrete spectrum .Mathematica ( Cluj ) 4 ( 27 ) , 253 – 260 ( 1962 ) . ( Russian ) Math . Rev . 29 #

6311 , 1182 ( 1965 ) . Theorems of comparison type for

**eigenvalues**of certainoperators ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero