A Hilbert space operator S is an element of B(H) is left m-invertible by T is an element
of B(H) ifSigma(m)(j=0) (-1)(m-j) ((m) (j)) (TSj)-S-j = 0,S is m-isometric if Sigma(m)(j=0)
(-1)(m-j) ((m) (j)) S*S-j(j) = 0and S is (m, C)-isometric for some conjugation C of
H ifSigma(m)(j=0) (-1)(m-j) ((m) (j)) S*(CSC)-C-j-C-j = 0.If a power bounded operator
S is left invertible by a power bounded operator T, then S (also, T*) is similar to
an isometry. Translated to m-isometric and (m, C)-isometric operators S this implies
that S is 1 -isometric, equivalently isometric, and (respectively) (1, C)-isometric.