Abstract
Let T be a bounded operator and let \(k \ge 2\) be an integer. We study in this paper the following question: T is a partial isometry implies that \(T^k\) is a partial isometry and conversely.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. Badea and M. Mbekhta, Operators similar to partial isometries, Acta Sci. Math. (Szeged) 71 (2005), 663–680.
S. L. Campbell, Linear operators for which \(T^*T\) and \(TT^*\) commute, Pacific J. Math. 34 (1972), 177–180.
B. P. Duggal, C. S. Kubrusley, and N. Levan, Contractions of class Q and invariant subspaces, Bull. Korean Math. Soc. 42 (2005), 169–177.
Ivan Erdelyi, Partial isometries closed under multiplication on Hilbert spaces, J. Math. Anal. Appl. 22 (1968), 546–551.
T. Furuta and R. Nakamoto, Some theorems on certain contraction operators, Proc. Japan Acad. Ser. A Math. Sci. 45 (1969), 565–567.
T. Furuta, Applications of the polar decomposition of an operator, Yokohama Math. J. 32 (1984), 245–253.
T. Furuta, On partial isometries, Proc. Japan Acad. Ser. A Math. Sci. 53 (1977), 95–97.
B. C. Gupta, A note on partial sometries. II, Indian J. Pure Appl. Math. 11 (1980), 208–211.
P. R. Halmos and L. J. Wallen, Powers of partial isometries, J. Math. Mech. 19 (1969/1970), 657–663.
I.H. Jeon, S.H. Kim, E. Ko, and J. E. Park, On positive-normal operators, Bull. Korean Math. Soc. 39 (2002), 33–41.
C.S. Kubrusly and B.P. Duggal On posinormal operators, Adv. Math. Sci. Appl. 17 (2007), 131–147.
C. S. Kubrusly, Contractions T for which A is a projection, Acta Sci. Math. (Szeged) 80 (2014), 603–624.
M. Mbekhta, Partial isometries and generalized inverses, Acta Sci. Math. (Szeged) 70 (2004), 767–781.
S. M. Patel, A note on quasi-isometries, Glasnik Matematic̆ki 35 (2000), 307–312.
S. M. Patel, 2-isometric operators, Glasnik Matematic̆ki 37 (2002), 143–147.
A.I.Popov and H. Radjavi, Semigroups of partial isometries, Semigroup Forum 87 (2013), 663–678.
H. C. Rhaly, Posinormal operators, J. Math. Soc. Japan 46 (1994), 587–605.
A. L. Shields, Weighted shift operators and analytic function theory, In: Topics in Operator Theory, pp. 49–128, Math. Surveys, No. 13, Amer. Math. Soc., Providence, R.I., 1974.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work is supported by the Labex CEMPI (ANR-11-LABX-0007-01), the Project URAC 03 of the National center of research and the Hassan II academy of sciences.
Rights and permissions
About this article
Cite this article
Ezzahraoui, H., Mbekhta, M., Salhi, A. et al. A note on roots and powers of partial isometries. Arch. Math. 110, 251–259 (2018). https://doi.org/10.1007/s00013-017-1116-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-017-1116-2