A closed densely defined operator $T$ such that both $T$ and $T^{\ast }$ are injective and paranormal yet $T$ is not normal

Abstract

In this note, we give an example of a densely defined closed one-to-one paranormal operator $T$ whose adjoint is also injective and paranormal, but $T$ fails to be normal.

References in corpus (1)

• Simple examples of non closable paranormal operators