Simultaneous unitary equivalence to bi-Carleman operators with arbitrarily smooth kernels of Mercer type

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70838In this paper, we characterize the families of those bounded linear operators on a separable Hilbert space which are simultaneously unitarily equivalent to integral bi-Carleman operators on $L_2(R)$ having arbitrarily smooth kernels of Mercer type. The main result is a qualitative sharpening of an earlier result of [7].10 pagesSpectral TheoryFunctional Analysis47B38; 47G10; 45P05Simultaneous unitary equivalence to bi-Carleman operators with arbitrarily smooth kernels of Mercer typetext