Abstract
A Hilbert space operator is left m-invertible by
if
S is m-isometric if
and S is
-isometric for some conjugation C of
if
If a power bounded operator S is left invertible by a power bounded operator T, then S (also,
) is similar to an isometry. Translated to m-isometric and
-isometric operators S this implies that S is 1-isometric, equivalently isometric, and (respectively)
-isometric.
AMS(MOS) subject classification (2010):
Disclosure statement
No potential conflict of interest was reported by the authors.