Possible extensions of the noncommutative integral

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Abstract

In this paper we will discuss the problem of extending a trace σ defined on a dense von Neumann subalgebraMof a topological *-algebra A to some subspaces of A. Inparticular, we will prove that extensions of the trace σ that go beyond the space L1(σ ) reallyexist and we will explicitly construct one of these extensions. We will continue the analysisundertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the generalproblem of extending positive linear functionals on a *-algebra
Original languageEnglish
Number of pages0
JournalRendiconti del Circolo Matematico di Palermo
Volume57
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • General Mathematics

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