## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2130

The notions of order are most closely tied to real

theoretic notions are simpler for complex

employ the following construction . If X is a real B - space which is ordered by < ,

let X1 ...

The notions of order are most closely tied to real

**coefficients**, while spectraltheoretic notions are simpler for complex

**coefficients**. To bridge this gap , weemploy the following construction . If X is a real B - space which is ordered by < ,

let X1 ...

Page 2323

... the

become the same as the

etu + bpe - lu + cp of the matrix ( ÔNak ) defined by the equations Ñ dx = di , mi

wome ...

... the

**coefficients**ap , bp , Cp of the terms of order p in the determinant N ( u )become the same as the

**coefficients**ap , bp , Cp in the determinant Ñ ( u ) = a ,etu + bpe - lu + cp of the matrix ( ÔNak ) defined by the equations Ñ dx = di , mi

wome ...

Page 2491

my poco še + fole ) + Žetale ) , the

dependence on the parameter € being analytic “ uniformly in t ” in a sense to be

specified more exactly below . The operators Te are supposed to be defined on

an ...

my poco še + fole ) + Žetale ) , the

**coefficients**p and qı being real , and thedependence on the parameter € being analytic “ uniformly in t ” in a sense to be

specified more exactly below . The operators Te are supposed to be defined on

an ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero