Journal of Operator Theory

Volume 89, Issue 2, Spring 2023 pp. 343-348.

Kernels of Hilbert module maps: a counterexample

Authors: Jens Kaad (1), Michael Skeide (2)
Author institution: (1) Department of Mathematics and Computer Science, University of Southern Denmark, Odense, 5230, Denmark
(2) Dipartimento di Economia, Universita degli Studi del Molise, Campobasso, 86100, Italy

Summary: 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.

DOI: http://dx.doi.org/10.7900/jot.2021jun11.2338
Keywords: Hilbert modules, kernels, right linear bounded maps, orthogonal complement, hereditary subalgebra

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