Unitary equivalence to integral operators

Sunder, V. S. (1981) Unitary equivalence to integral operators Pacfic Journal of Mathematics, 92 (1). pp. 211-215. ISSN 0030-8730

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A bounded operator A on L2(X) is called an integral operator if there exists a measurable function k on X x X such that, for each f) in L 2(X), ∫\k(x,y)ƒ(y)\d μ (y) < ∞ a.e. and Aƒ(x)= ∫ k(x,y)ƒ(y)d μ (y) a.e. (Throughout this paper, (X, μ ) will denote a separable, sigma -finite measure space which is not purely atomic.) An integral operator is called a Carleman operator if the inducing kernel k satisfies the stronger requirement: ∫\k(x,y)\ 2d μ (y) < ∞ for almost every x in X.

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