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On the operator equation \(AX=XV^*\). (English) Zbl 0674.47008

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.
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