Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SUPERCYCLICITY OF JOINT ISOMETRIES

  • ANSARI, MOHAMMAD (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY) ;
  • HEDAYATIAN, KARIM (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY) ;
  • KHANI-ROBATI, BAHRAM (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY) ;
  • MORADI, ABBAS (DEPARTMENT OF MATHEMATICS COLLEGE OF SCIENCES SHIRAZ UNIVERSITY)
  • Received : 2014.06.11
  • Published : 2015.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Let H be a separable complex Hilbert space. A commuting tuple $T=(T_1,{\cdots},T_n)$ of bounded linear operators on H is called a spherical isometry if $\sum_{i=1}^{n}T^*_iT_i=I$. The tuple T is called a toral isometry if each $T_i$ is an isometry. In this paper, we show that for each $n{\geq}1$ there is a supercyclic n-tuple of spherical isometries on $\mathbb{C}^n$ and there is no spherical or toral isometric tuple of operators on an infinite-dimensional Hilbert space.

Keywords

Acknowledgement

Supported by : Shiraz University Research Council

References

  1. A. Athavale, On the intertwining of joint isometries, J. Operator Theory 23 (1990), no. 2, 339-350.
  2. M. Faghih Ahmadi and K. Hedayatian, Hypercyclicity and supercyclicity of m-isometric operators, Rocky Mountain J. Math. 42 (2012), no. 1, 15-23. https://doi.org/10.1216/RMJ-2012-42-1-15
  3. N. S. Feldman, Hypercyclic pairs of coanalytic Toeplitz operators, Integral Equations Operator Theory 58 (2007), no. 2, 153-173. https://doi.org/10.1007/s00020-007-1484-2
  4. N. S. Feldman, Hypercyclic tuples of operators and somewhere dense orbits, J. Math. Anal. Appl. 346 (2008), no. 1, 82-98. https://doi.org/10.1016/j.jmaa.2008.04.027
  5. H. M. Hilden and L. J. Wallen, Some cyclic and non-cyclic vectors of certain operators, Indiana Univ. Math. J. 23 (1973/74), 557-565. https://doi.org/10.1512/iumj.1974.23.23046
  6. R. Soltani, K. Hedayatian, and B. Khani Robati, On supercyclicity of tuples of operators, to appear in the Bull. Malays. Math. Sci. Soc.
  7. R. Soltani, B. Khani Robati, and K. Hedayatian, Hypercyclic tuples of the adjoint of the weighted composition operators, Turkish J. Math. 36 (2012), no. 3, 452-462.