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Kubrusly","submitted_at":"2019-03-08T13:17:27Z","abstract_excerpt":"A Hilbert space operator $S\\in\\B$ is left $m$-invertible by $T\\in\\B$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right)T^jS^j}=0,$$ $S$ is $m$-isometric if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jS^j}=0$$ and $S$ is $(m,C)$-isometric for some conjugation $C$ of $\\H$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jCS^jC}=0.$$ If a power bounded operator $S$ is left invertible by a power bounded operator $T$, then $S$ (also, $T^*$) is similar to an isometry. 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Duggal, C.S. Kubrusly","submitted_at":"2019-03-08T13:17:27Z","abstract_excerpt":"A Hilbert space operator $S\\in\\B$ is left $m$-invertible by $T\\in\\B$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right)T^jS^j}=0,$$ $S$ is $m$-isometric if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jS^j}=0$$ and $S$ is $(m,C)$-isometric for some conjugation $C$ of $\\H$ if $$\\sum_{j=0}^m{(-1)^{m-j}\\left(\\begin{array}{clcr}m\\\\j\\end{array}\\right){S^*}^jCS^jC}=0.$$ If a power bounded operator $S$ is left invertible by a power bounded operator $T$, then $S$ (also, $T^*$) is similar to an isometry. 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