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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:472

Article

Lesch, Matthias¹  Mesland, Bram¹ 

[1] Univ Bonn, Math Inst, Endenicher Allee 60, D-53115 Bonn, Germany

关键词: Hilbert-C*-module;    Regular operator;    KK-theory;   

DOI  :  10.1016/j.jmaa.2018.11.059

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free