Tensor product of Fredholm operators on nonarchimedean Banach spaces (Q2266420)

By using a technique of R. Schatten and A. W. Ingleton's non-archimedean version of the Hahn-Banach theorem the author derives several lemmata which finally yield the following theorem: let X, Y, be non-archimedeanly (n.-a.) normed Banach spaces over a spherically complete n.-a. and non- trivially valuated field F, and \(T:\quad X\to Y\) a Fredholm operator, then, for every finite dimension n.-a. Banach space M over F, the tensor product \(T{\hat \otimes}I_ M\) is also Fredholm and its index \(ind(T{\hat \otimes}I_ M)=\dim (\ker (T{\hat \otimes}I_ M)-\dim (co\ker (T{\hat \otimes}I_ M))\) equals \(ind(T).\dim (M).\) Unfortunately, the author neither gives a motivation nor applications, therefore the result seems somewhat ''technical'' and interesting mainly for highly specialized functional analysts.