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. In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra
TRIOLO, S. (2011). Possible extensions of the noncommutative integral. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 57(1) [10.1007/s12215-011-0063-1].
Possible extensions of the noncommutative integral
TRIOLO, Salvatore
2011-01-01
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. In particular, we will prove that extensions of the trace σ that go beyond the space L1(σ ) really exist and we will explicitly construct one of these extensions. We will continue the analysis undertaken in Bongiorno et al. (Rocky Mt. J. Math. 40(6):1745–1777, 2010) on the general problem of extending positive linear functionals on a *-algebra
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