A pointwise spectrum and representation of operators
Authors:
N. Bertoglio, Servet Martínez and Jaime San Martín
Journal:
Proc. Amer. Math. Soc. 126 (1998), 375382
MSC (1991):
Primary 47A11, 47D15
MathSciNet review:
1459108
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Abstract: For a selfadjoint 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 1703, Correo 3, Santiago, Chile
Email:
smartine@dim.uchile.cl
Jaime San Martín
Email:
jsanmart@dim.uchile.cl
DOI:
http://dx.doi.org/10.1090/S0002993998044281
PII:
S 00029939(98)044281
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
