Previous issue ·  Next issue ·  Recently posted articles ·  Most recent issue · All issues   
Home Overview Authors Editorial Contact Subscribe

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.

Keywords:  Hilbert modules, kernels, right linear bounded maps, orthogonal complement, hereditary subalgebra

Contents   Full-Text PDF