Jocić, Danko A characterization of formally symmetric unbounded operators. (English) Zbl 0701.47010 Publ. Inst. Math., Nouv. Sér. 46(60), 141-144 (1989). The main result is: If A, B are symmetric operators on a Hilbert space, such that D(A)\(\subset D(B)\), \(D(A^*)\subset D(B^*)\) and \(\| (A^*-iB^*)x\| \leq \| A^*x\|\) on \(D(A^*)\), then \(B\subset 0\). Hence, criteria for an unbounded operator T to be formally symmetric (i.e. \(Tx=T^*x\) for x in \(D(T)\cap D(T^*))\), symmetric, or selfadjoint are obtained. Reviewer: N.Angelescu MSC: 47B25 Linear symmetric and selfadjoint operators (unbounded) 47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.) Keywords:symmetric operators on a Hilbert space; unbounded operator; formally symmetric PDFBibTeX XMLCite \textit{D. Jocić}, Publ. Inst. Math., Nouv. Sér. 46(60), 141--144 (1989; Zbl 0701.47010) Full Text: EuDML