Sums of regular selfadjoint 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.

arXiv commentFinal version. Minor editorial changes

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• A local global principle for regular operators in Hilbert C*-modules
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Cited by in corpus (9)

• Gauge theory on noncommutative Riemannian principal bundles
• Index theory and topological phases of aperiodic lattices
• On the Unbounded Picture of $KK$-Theory
• Injective tensor products in strict deformation quantization
• Transversals, duality, and irrational rotation
• Localisations of half-closed modules and the unbounded Kasparov product
• Generalised Dirac-Schrödinger operators and the Callias Theorem
• Addendum to: Indefinite Kasparov modules and pseudo-Riemannian manifolds
• Dirac-Schrödinger operators, index theory, and spectral flow