Abstract
Kucerovsky's theorem provides a method for recognizing the interior Kasparov product of selfadjoint unbounded cycles. In this paper we present a partial extension of Kucerovsky's theorem to the non-selfadjoint setting by replacing unbounded Kasparov modules with Hilsum's half-closed chains. On our way we show that any half-closed chain gives rise to a multitude of twisted selfadjoint unbounded cycles via a localization procedure. These unbounded modular cycles allow us to provide verifiable criteria avoiding any reference to domains of adjoints of symmetric unbounded operators.
Original language | English |
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Journal | Journal of Operator Theory |
Volume | 82 |
Issue number | 1 |
Pages (from-to) | 115-145 |
Number of pages | 31 |
ISSN | 0379-4024 |
DOIs | |
Publication status | Published - Jun 2019 |
Keywords
- Half-closed chains
- Kasparov product
- KK-theory
- Unbounded Kasparov modules
- Unbounded Kasparov product
- Unbounded KK-theory
- Unbounded modular cycles