ArticleOriginal scientific text

Title

A quasi-nilpotent operator with reflexive commutant, II

Authors 1, 2

Affiliations

  1. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
  2. epartment of Mathematics, Faculty of Electrical Engineering, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava, Slovak Republic

Abstract

A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. The norms |Tn| converge to zero arbitrarily fast.

Keywords

quasinilpotent operator, commutant, reflexivity

Bibliography

  1. Š. Drahovský and M. Zajac, Hyperreflexive operators on finite dimensional Hilbert spaces, Math. Bohem. 118 (1993), 249-254.
  2. D. Hadwin and E. A. Nordgren, Reflexivity and direct sums, Acta Sci. Math. (Szeged) 55 (1991), 181-197.
  3. D. A. Herrero, A dense set of operators with tiny commutants, Trans. Amer. Math. Soc. 327 (1991), 159-183.
  4. W. R. Wogen, On cyclicity of commutants, Integral Equations Operator Theory 5 (1982), 141-143.
  5. M. Zajac, A quasi-nilpotent operator with reflexive commutant, Studia Math. 118 (1996), 277-283.
  6. M. Zajac, Rate of convergence to zero of powers of an hyper-reflexive operator, in: Proceedings of Workshop on Functional Analysis and its Applications in Mathematical Physics and Optimal Control (Nemecká, 1997).
Pages:
173-177
Main language of publication
English
Received
1998-03-31
Published
1999
Exact and natural sciences