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

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Page 1938

N and an operator S which is of

definition . + 1 DEFINITION . A bounded operator S is said to be of

case it is a

E is ...

N and an operator S which is of

**scalar type**in accordance with the followingdefinition . + 1 DEFINITION . A bounded operator S is said to be of

**scalar type**incase it is a

**spectral**operator which satisfies the equation S = S XE ( da ) , whereE is ...

Page 2174

Theodore Schwartz ... that lett | S M for all t e R implies that T is equivalent to a

self adjoint operator and hence is a

**Spectral**Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, JacobTheodore Schwartz ... that lett | S M for all t e R implies that T is equivalent to a

self adjoint operator and hence is a

**scalar type**operator with real**spectrum**.Page 2242

An unbounded

identity for T in the sense of Definition 12 is the same as the resolution of the

identity ...

An unbounded

**spectral**operator of**scalar type**in the sense of Definition 12 is a**spectral**operator in the sense of Definition 1 . Moreover , the resolution of theidentity for T in the sense of Definition 12 is the same as the resolution of the

identity ...

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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