A new method for comparing two Norm Hilbert spaces and their operators

Abstract

The paper deals with operators on Norm Hilbert spaces over a Krull valued field K. By using carefully selected equivalent norms (i) the perturbation theory of Fredholm operators (see Ochsenius and Schikhof (2010) [7]) is completed, and (ii) new matrix characterizations of operators are derived (compare Ochsenius and Schikhof (2007) [6]). For a prominent E, the first infinite-dimensional orthomodular space in history constructed by Keller (1980) [1], this leads to simple and elegant characterizations. (C) 2011 Royal Netherlands Academy of Arts and Sciences. Published by Elsevier B.V. All rights reserved.