On a theorem of Kucerovsky for half-closed chains

Jens Kaad, Walter D. Van Suijlekom

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

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.

OriginalsprogEngelsk
TidsskriftJournal of Operator Theory
Vol/bind82
Udgave nummer1
Sider (fra-til)115-145
Antal sider31
ISSN0379-4024
DOI
StatusUdgivet - jun. 2019

Fingeraftryk

Cycle
Closed
Theorem
Symmetric Operator
Unbounded Operators
Interior
Partial
Module

Citer dette

Kaad, Jens ; Van Suijlekom, Walter D. / On a theorem of Kucerovsky for half-closed chains. I: Journal of Operator Theory. 2019 ; Bind 82, Nr. 1. s. 115-145.
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On a theorem of Kucerovsky for half-closed chains. / Kaad, Jens; Van Suijlekom, Walter D.

I: Journal of Operator Theory, Bind 82, Nr. 1, 06.2019, s. 115-145.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - On a theorem of Kucerovsky for half-closed chains

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AU - Van Suijlekom, Walter D.

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N2 - 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.

AB - 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.

KW - Half-closed chains

KW - Kasparov product

KW - KK-theory

KW - Unbounded Kasparov modules

KW - Unbounded Kasparov product

KW - Unbounded KK-theory

KW - Unbounded modular cycles

U2 - 10.7900/jot.2018mar07.2208

DO - 10.7900/jot.2018mar07.2208

M3 - Journal article

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JO - Journal of Operator Theory

JF - Journal of Operator Theory

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