# SUPERCYCLICITY OF TWO-ISOMETRIES

• Ahmadi, M. Faghih (Department of Mathematics, College of Sciences, Shiraz University) ;
• Hedayatian, K. (Department of Mathematics, College of Sciences, Shiraz University)
• Accepted : 2008.01.07
• Published : 2008.03.25

#### Abstract

A bounded linear operator T on a complex separable Hilbert space H is called a two-isometry, if $T^{*2}T^2-2T^*T+1=0$. In this paper it is shown that every two-isometry is not supercyclic. This generalizes a result due to Ansari and Bourdon.

#### References

1. J. Agler and M. Stankus, m-isometric transformation of Hilbert space I, Integr. Equ. Oper. Theory, 21(1995), 383-429. https://doi.org/10.1007/BF01222016
2. S. I. Ansari and P. S. Bourdon, Some properties of cyclic operators, Acta Sci. Math. (Szeged) 63 (1997), 195-207.
3. N. S. Feldman, N-supercyclic operators, Studia Math. 151 (2002), 141-159. https://doi.org/10.4064/sm151-2-3
4. N. S. Feldman, The dynamics of cohyponormal operators, Trends in Banach spaces and operator theory (Proc. Conf., Memphis, TN, 2001), 71-85, Amer. Math. Soc., Providence, RI, 2003.
5. K. G. Grosse-Erdmann, Recent developments in hypercyclicity, Rev. R. Acad. Cien. Serie A. Mat. Vol. 79 (2), 2003, 273-289.
6. K. Hedayatian, On cyclicity in the space $H^p({\beta})$, Taiwanese Journal of Mathematics, Vol. 8, No.3, (2004) 429-442. https://doi.org/10.11650/twjm/1500407663
7. F. Leon Saavedra, the positive supercyclicity theorem, Extracta Mathematicae, Vol. 19 Num. 1, (2004), 145-149.
8. A. Peris and L. Saldivia, Syndetically hypercyclic operators, Integr. Equ. Oper. Theory, Vol. 51, No. 2 (2005) 275-281. https://doi.org/10.1007/s00020-003-1253-9
9. S. Richter, A representation theorem for cyclic analytic two-isometries, Trans. Amer. Math. Soc. 328 (1991), 325-349. https://doi.org/10.2307/2001885

#### Cited by

1. Powers of A-m-Isometric Operators and Their Supercyclicity vol.39, pp.3, 2016, https://doi.org/10.1007/s40840-015-0201-6