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

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Page 2118

A generalized scalar operator Te B ( X ) is said to be

spectral distribution . Although it is not known whether or not every generalized

scalar operator is

two ...

A generalized scalar operator Te B ( X ) is said to be

**regular**if it has a**regular**spectral distribution . Although it is not known whether or not every generalized

scalar operator is

**regular**( unless the spectrum is sufficiently " thin " ) , given anytwo ...

Page 2158

If the set of points

subinterval of l ' , whose end points are

Borel subset of the plane is measurable T. PROOF . Let y be a closed subinterval

of F ...

If the set of points

**regular**relative to T is dense on To , then every closedsubinterval of l ' , whose end points are

**regular**relative to T is in S ( T ) and everyBorel subset of the plane is measurable T. PROOF . Let y be a closed subinterval

of F ...

Page 2160

If X is reflexive and if the adjoint T * satisfies the boundedness condition ( B ) ,

then the

interval of constancy relative to T consists entirely of

view of ...

If X is reflexive and if the adjoint T * satisfies the boundedness condition ( B ) ,

then the

**regular**points relative to T are dense in To and , in particular , everyinterval of constancy relative to T consists entirely of

**regular**points . PROOF . Inview of ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

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 discrete 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