Proximity Between Selfadjoint Operators and Between Their Associated Random Measures

Authors

  • Alain Boudou Institut de Mathématiques de Toulouse Université Paul Sabatier 31062 Toulouse
  • Sylvie Viguier-Pla Université de Perpignan Via Domitia and Université Paul Sabatier Toulouse

DOI:

https://doi.org/10.29020/nybg.ejpam.v11i4.2552

Keywords:

Random measures, Stationary processes, Convolution, Spectral measures

Abstract

We study how the proximity between two
selfadjoint bounded operators, measured by a classical distance, can
be expressed by a proximity between the associated spectral
measures. This last proximity is based on a partial order relation on the set
of projectors. Assuming an hypothesis of commutativity, we show that
the proximity between operators implies the one between the
associated spectral measures, and conversally, the proximity between
spectral measures implies the one between associated selfadjoint operators.

Author Biographies

  • Alain Boudou, Institut de Mathématiques de Toulouse Université Paul Sabatier 31062 Toulouse
    HDR
  • Sylvie Viguier-Pla, Université de Perpignan Via Domitia and Université Paul Sabatier Toulouse
    Institut de Mathematiques de Toulouse Assistant Professor, HDR

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Published

2018-10-24

Issue

Vol. 11 No. 4: (October 2018)

Section

Mathematical Statistics

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How to Cite

Proximity Between Selfadjoint Operators and Between Their Associated Random Measures. (2018). European Journal of Pure and Applied Mathematics, 11(4), 893-910. https://doi.org/10.29020/nybg.ejpam.v11i4.2552