ACTA issues

## On jointly essentially self-adjoint tuples of operators

Jörg Eschmeier, Florian-Horia Vasilescu

Acta Sci. Math. (Szeged) 67:1-2(2001), 373-386
2789/2009

 Abstract. Let $S = (S_1,\ldots, S_n)$ be a tuple of symmetric operators $S_j\colon D(S_j)\subset H\rightarrow H$ on a Hilbert space $H$. We show that $S$ is jointly essentially self-adjoint in the sense of Fuglede if and only if a suitable associated matrix operator is essentially self-adjoint as a single operator. As an application we obtain an elementary proof of Nelson's famous commutativity criterion for essentially self-adjoint operators. AMS Subject Classification (1991): 47B25, 47B15 Received December 2, 1999. (Registered under 2789/2009.)