Paracomplete normed spaces and Fredholm theory
A normed space is called paracomplete, if it admits another norm and it is complete with respect to that norm. The authors prove: A normed space \(X\) is paracomplete if and only if the algebra \(L(X)\) of all continuous linear operators acting in \(X\) is paracomplete. Consequently all operators in \(L(X)\) have compact spectra if \(X\) is paracomplete. Further the authors characterize the closed linear operators between paracomplete spaces, which are Fredholm operators, and the linear continuous operators between normed spaces, which are almost semi-Fredholm operators in the sense of R.~Harte.
scientific article; zbMATH DE number 1339484
scientific article