کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4589595 | 1334889 | 2016 | 79 صفحه PDF | دانلود رایگان |
We consider the general properties of bounded approximate units in non-self-adjoint operator algebras. Such algebras arise naturally from the differential structure of spectral triples and unbounded Kasparov modules. Our results allow us to present a unified approach to characterising completeness of spectral metric spaces, existence of connections on modules, self-adjointness and regularity of induced operators on tensor product C⁎C⁎-modules and the lifting of Kasparov products to the unbounded category. In particular, we prove novel existence results for quasicentral approximate units in non-self-adjoint operator algebras, allowing us to strengthen Kasparov's technical theorem and extend it to this realm. Finally, we show that given any two composable KK-classes, we can find unbounded representatives whose product can be constructed to yield an unbounded representative of the Kasparov product.
Journal: Journal of Functional Analysis - Volume 271, Issue 9, 1 November 2016, Pages 2460–2538