Talk:Integral linear operator
Add topicLatest comment: 1 year ago by Csoler in topic Wrong statement
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Wrong statement
[edit]"every integral operator between two Hilbert spaces is nuclear.". This is wrong. I think that what Treves calls an "integral mapping" doesn't cover the entire notion of integral operators. It is pretty easy to forge non compact integral operators between Hilbert spaces. See for instance Kalisch, 1972 "On Operators on Separable Banach Spaces with Arbitrary Prescribed Point Spectrum". The paper constructs non compact integral operators on L^2([0,1]) which is also a Hilbert space. If the kernel of the integral operator is bounded or square-integrable then the operator is nuclear. A necessary condition is that its point spectrum is summable. Csoler (talk) 15:57, 23 January 2025 (UTC)