Kernels of Hilbert module maps: a counterexample

Jens Kaad*, Michael Skeide

*Kontaktforfatter

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Abstract

Answering a long standing question, we give an example of a Hilbert module and a nonzero bounded right linear map having a kernel with trivial orthogonal complement. In particular, this kernel is different from its own double orthogonal complement.

OriginalsprogEngelsk
TidsskriftJournal of Operator Theory
Vol/bind89
Udgave nummer2
Sider (fra-til)343-348
ISSN0379-4024
DOI
StatusUdgivet - 2023

Bibliografisk note

Funding Information:
This little note is an output of a talk by the second author at the “Hilbert C*-Modules Online Weekend” from December 5/6, 2020, presenting the open problem which was then answered by the first author. We are deeply grateful to the organizers of the Workshop Michael Frank, Vladimir Manuilov, and Evgenij Troitsky for having made this possible. We also acknowledge useful discussions with Michael Frank, Boris Guljas, and Orr Shalit.

Publisher Copyright:
© Copyright by THETA, 2023

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