On a theorem of Kucerovsky for half-closed chains

Jens Kaad, Walter D. Van Suijlekom

Research output: Contribution to journalJournal articleResearchpeer-review


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 languageEnglish
JournalJournal of Operator Theory
Issue number1
Pages (from-to)115-145
Number of pages31
Publication statusPublished - Jun 2019


  • Half-closed chains
  • Kasparov product
  • KK-theory
  • Unbounded Kasparov modules
  • Unbounded Kasparov product
  • Unbounded KK-theory
  • Unbounded modular cycles


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