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

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Results 1-3 of 51

Page 1925

The problem of extending this reduction theory to non -

of the most important unsolved problems in the theory of linear operations .

Consider , for instance , the problem of finding a resolution of the identity for the

formal ...

The problem of extending this reduction theory to non -

**normal**operators is oneof the most important unsolved problems in the theory of linear operations .

Consider , for instance , the problem of finding a resolution of the identity for the

formal ...

Page 1978

To illustrate more clearly the relationship between Theorem 6 and the well known

result for self adjoint operators , we observe that a self adjoint operator or , more

generally , a

To illustrate more clearly the relationship between Theorem 6 and the well known

result for self adjoint operators , we observe that a self adjoint operator or , more

generally , a

**normal**operator in AP is a spectral operator . For if A is a**normal**...Page 2538

On the distribution of the spectra of

Japan Acad . 37 , 464 – 468 ( 1961 ) . 2 . Simplification of the canonical spectral

representation of a

On the distribution of the spectra of

**normal**operators in Hilbert spaces . Proc .Japan Acad . 37 , 464 – 468 ( 1961 ) . 2 . Simplification of the canonical spectral

representation of a

**normal**operator in Hilbert space and its applications . Mem .### What people are saying - Write a review

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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