Abstract
Given an-dimensional right vector spaceV over a division ring\(\mathbb{K}\) we denote byS the semigroup of the endomorphisms ofV and designate this semigroup as alinear semigroup. First we prove that every automorphism ofS can be written asT→fTf −1, wheref∶V→V is a semilinear homeomorphism. Furthermore, we show that every isomorphism between maximal compact subsemigroups ofS is also of this type.
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