Kernels of Hilbert Module Maps: A Counterexample

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.

arXiv comment6 pages

References in corpus (3)

• CP-Semigroups and Dilations, Subproduct Systems and Superproduct Systems: The Multi-Parameter Case and Beyond
• On Hahn-Banach type theorems for Hilbert C*-modules
• Pure Semigroups of Isometries on Hilbert C*-Modules