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I have edited a bit at Fredholm operator. Also started a stubby Fredholm module in the process. But it remains very much unfinished. Have to interrupt now for a bit.
While still short, Fredholm operator is a very good entry!!! (well, I did a part in it, but the improvements are both essential and good and wellcome!)
a couple of recent reference items to add to Fredholm operator once the edit functionality is back:
Nikolai V. Ivanov, Topological categories related to Fredholm operators: I. Classifying spaces (arXiv:2111.14313)
Nikolai V. Ivanov, Topological categories related to Fredholm operators: II. The analytic index (arXiv:2111.15081)
The entry Fredholm operator is missing any reference for Atkinson’s theorem (i.e. that the definition of Fredholm operators via finite dim ker and coker is equivalent to invertibility up to compact and/or finite-rank operators). This here just to record some.
The original article is:
Early streamlined proof is in:
Michael Atiyah, Prop. A8 (p. 163) in: K-theory, Harvard Lecture 1964 (notes by D. W. Anderson), Benjamin 1967 (pdf)
Gerard J. Murphy, Theorem 2.1 in: Fredholm Index Theory and the Trace, Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences 94A 2 (1994), 161-166 (jstor:20489482 )
See also
Monographs/texbook accounts include:
Bernhelm Booß, p. 35-36 in: Topologie und Analysis, Springer (1977) (doi:10.1007/978-3-642-66752-7)
Nigel Higson, John Roe, 2.1.4 in: Analytic K-Homology, Oxford mathematical monographs, Oxford University Press (2000) (ISBN:9780198511762)
William Arveson, Theorem 3.3.2 in: A Short Course on Spectral Theory, Graduate Texts in Mathematics, 209, Springer (2002) (doi:10.1007/b97227)
Also need to add these references:
Marina Prokhorova, Spectral Sections, arXiv:2008.04672.
Marina Prokhorova, Spaces of unbounded Fredholm operators. I. Homotopy equivalences, arXiv:2110.14359.
Marina Prokhorova, The continuity properties of discrete-spectrum families of Fredholm operators, arXiv:2201.09869.
Marina Prokhorova, From graph to Riesz continuity, arXiv:2202.03337.
Added pointer to
and:
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