A pointwise spectrum

and representation of operators

Authors:
N. Bertoglio, Servet Martínez and Jaime San Martín

Journal:
Proc. Amer. Math. Soc. **126** (1998), 375-382

MSC (1991):
Primary 47A11, 47D15

DOI:
https://doi.org/10.1090/S0002-9939-98-04428-1

MathSciNet review:
1459108

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Abstract | References | Similar Articles | Additional Information

Abstract: For a self-adjoint operator commuting with an increasing family of projections we study the multifunction an open set of the topology containing , where is the spectrum of on . Let be the measure of maximal spectral type. We study the condition that is essentially a singleton, is not a singleton. We show that if is the density topology and if satisfies the density theorem, in particular if it is absolutely continuous with respect to the Lebesgue measure, then this condition is equivalent to the fact that is a Borel function of . If is the usual topology then the condition is equivalent to the fact that is approched in norm by step functions , where the set of intervals covers the set where is a singleton.

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Additional Information

**N. Bertoglio**

Affiliation:
Facultad de Matemática, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22, Santiago, Chile

Email:
nbertogl@riemann.mat.puc.cl

**Servet Martínez**

Affiliation:
Universidad de Chile, Facultad de Ciencias Físicas y Matemáticas, Departamento de Ingeniería Matemática, Casilla 170-3, Correo 3, Santiago, Chile

Email:
smartine@dim.uchile.cl

**Jaime San Martín**

Email:
jsanmart@dim.uchile.cl

DOI:
https://doi.org/10.1090/S0002-9939-98-04428-1

Received by editor(s):
July 20, 1995

Received by editor(s) in revised form:
April 30, 1996

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1998
American Mathematical Society