Professor Irina Mitrea and collaborators have recently published Fredholm Theory on Topological Vector Spaces in the Springer Monographs in Mathematics series. 

The monograph investigates the extent to which the classical Riesz and Fredholm theories extend beyond their traditional setting of Banach and Hilbert spaces, in the much broader context of topological vector spaces. A central theme is that local convexity, and the availability of continuous linear functionals, are far less indispensable than the existing literature might suggest. As such, this work reveals a striking resilience and robustness of classical operator theory and provides new insights into how far its fundamental principles can be extended.