Kittaneh, Fuad On the operator equation \(AX=XV^*\). (English) Zbl 0674.47008 Chin. J. Math. 16, No. 1, 29-40 (1988). Let H be a separable complex Hilbert space. B(H) the algebra of all bounded linear operators acting in H. Several conditions are given on \(A\in B(H)\) under which the equation \(AX=XV^*\), where V is an isometry on H, has only the trivial solution. The generalized Toeplitz operators are studied, among others, a generalization of the fact that the only compact Toeplitz operator is the zero one is also presented. Reviewer: J.Kolomy MSC: 47A62 Equations involving linear operators, with operator unknowns 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B20 Subnormal operators, hyponormal operators, etc. Keywords:hyponormal operator; isometry; unilateral shift; generalized Toeplitz operators PDFBibTeX XMLCite \textit{F. Kittaneh}, Chin. J. Math. 16, No. 1, 29--40 (1988; Zbl 0674.47008)