The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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ON SPECTRA OF 2-ISOMETRIC OPERATORS

  • Yang, Young-Oh (DEPARTMENT OF MATHEMATICS AND INFORMATION, CHEJU NATIONAL UNIVERSITY) ;
  • Kim, Cheoul-Jun (DEPARTMENT OF MATHEMATICS AND INFORMATION, CHEJU NATIONAL UNIVERSITY)
  • Published : 2009.08.31
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Abstract

A Hilbert space operator T is a 2-isometry if $T^{{\ast}2}T^2\;-\;2T^{\ast}T+I$ = O. We shall study some properties of 2-isometries, in particular spectra of a non-unitary 2-isometry and give an example. Also we prove with alternate argument that the Weyl's theorem holds for 2-isometries.

Keywords

References

  1. J. Agler & M. Stankus: m-isometric transformations of Hilbert space I. Integral Equations and Operator Theory 21 (1995), 383-429. https://doi.org/10.1007/BF01222016
  2. S. K. Berberian: Introduction to Hilbert space. Oxford University Press, 1961.
  3. S. K. Berberian : The Weyl spectrum of an operator. Indiana Univ. Math. J. 20 (1970), 529-544. https://doi.org/10.1512/iumj.1970.20.20044
  4. J. B. Conway: A course in functional analysis. Springer-Verlag, New York, 1985.
  5. K. K. Oberai: On the Weyl spectrum. Illinois J. Math. 18 (1974), 208-212.
  6. S. M. Patel: 2-isometric operators. Glasnik Mathematicki 37 (2002), no. 57, 143-147.