A characterization of positive normal functionals on the full operator algebra

2017/10/18 by Sebestyén, Zoltán, Tarcsay, Zsigmond, Titkos, Tamás
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1710.06830

Abstract

Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full operator algebra is normal. We also characterize those functionals defined on the left ideal of finite rank operators that have a normal extension.

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