## Linear Operators: Spectral operators |

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Page 2118

A generalized scalar operator T e 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 T e 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 To whose end points are

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

of T ...

If the set of points

**regular**relative to T is dense on To , then every closedsubinterval of To 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 T ...

Page 2344

In this connection , it is also worth making a simple remark on the notion of

the boundary conditions are written in the normalized way described in the

paragraph ...

In this connection , it is also worth making a simple remark on the notion of

**regular**boundary conditions in the case of a second order differential operator . Ifthe boundary conditions are written in the normalized way described in the

paragraph ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm 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 uniform uniformly unique valued vector weakly zero