Integral operators generated by H-continuous measures (Q909220)

Let X be a separable Hilbert space and let H be a linear subspace in X. The author introduces the notion of H-compact operator and the notion of H-continuous measure. The main result says that if \(\mu\) is a real-valued measure on X with bounded variation, then \(\mu\) is H-continuous if and only if the operator \[ (Q_{\mu}f)(x)=\int_{X}f(x-y)d\mu (x) \] is H- compact.