Integral representations of closed operators as bi-Carleman operators with arbitrarily smooth kernels

2004/04/13 by Igor M. Novitskii, Novitskii, Igor M.
Mathematics · #45P05 #47B38 #47G10 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.FA #math.SP #msc:45P05 #msc:47B38 #msc:47G10

paper · pdf · doi:10.48550/arxiv.math/0404244

LaTeX file, 10 pages

arxiv created 2004/04/13 · openalex publication_date 2004/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in L₂(R) with bounded and arbitrarily smooth kernel on R². In addition, we give an explicit construction of corresponding unitary operators. The main result is a qualitative sharpening of an earlier result of [5].

Related

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