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

2004/04/12 by Igor M. Novitskii, Novitskii, Igor M.
Mathematics · #45P05 #47B38 #47G10 #FOS: Mathematics #Functional Analysis (math.FA) #Spectral Theory (math.SP) #math.FA #math.SP #msc:45P05 #msc:47B38 #msc:47G10

paper · pdf · doi:10.48550/arxiv.math/0404228

10 pages

arxiv created 2004/04/12 · arxiv updated 2009/12/01

Abstract

In 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 L₂(R) having arbitrarily smooth kernels of Mercer type. The main result is a qualitative sharpening of an earlier result of [7].

Related

• Simultaneous unitary equivalence to Carleman operators with arbitrarily smooth kernels
• Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels
• Integral operators with infinitely smooth bi-Carleman kernels of Mercer type
• Integral representations of unbounded operators by arbitrarily smooth Carleman kernels
• An extension of Mercer's theorem to unbounded operators