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

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Results 1-3 of 67

Page 1930

A spectral measure E is said to be countably additive if for each 2 * in X * and

each x in X the scalar set function x * E ( ) x is countably additive on the

E. → 4 COROLLARY . If the

A spectral measure E is said to be countably additive if for each 2 * in X * and

each x in X the scalar set function x * E ( ) x is countably additive on the

**domain**ofE. → 4 COROLLARY . If the

**domain**of a countably 1930 XV.2.2 xv . SPECTRAL ...Page 1931

If the

countably additive in the strong operator topology and bounded . The

boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 . The spectral

operators in ...

If the

**domain**of a countably additive spectral measure E is a o - field , then E iscountably additive in the strong operator topology and bounded . The

boundedness of E ( o ) follows from Corollaries IV.10.2 and II.3.21 . The spectral

operators in ...

Page 2256

where C , is a finite collection of closed Jordan curves bounding a

containing the union of o ( T ) and a neighborhood of infinity , C , being oriented

in the customary positive sense of complex variable theory . The curves C of the ...

where C , is a finite collection of closed Jordan curves bounding a

**domain**Dicontaining the union of o ( T ) and a neighborhood of infinity , C , being oriented

in the customary positive sense of complex variable theory . The curves C of the ...

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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