Sums of regular self-adjoint operators in Hilbert-C*-modules

Abstract

We introduce a notion of weak anticommutativity for a pair (S, T) of self-adjoint regular operators in a Hilbert C*-module E. We prove that the sum S T of such pairs is self-adjoint and regular on the intersection of their domains. A similar result then holds for the sum S-2 + T-2 of the squares. We show that our definition is closely related to the Connes-Skandalis positivity criterion in KK-theory. As such we weaken a sufficient condition of Kucerovsky for representing the Kasparov product. Our proofs indicate that our conditions are close to optimal. (C) 2018 Elsevier Inc. All rights reserved.