A quasi-nilpotent operator with reflexive commutant, II

V. Müller; M. Zając

Studia Mathematica (1999)

  • Volume: 132, Issue: 2, page 173-177
  • ISSN: 0039-3223

Abstract

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

How to cite

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Müller, V., and Zając, M.. "A quasi-nilpotent operator with reflexive commutant, II." Studia Mathematica 132.2 (1999): 173-177. <http://eudml.org/doc/216593>.

@article{Müller1999,
abstract = {A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. The norms $|T^n|$ converge to zero arbitrarily fast.},
author = {Müller, V., Zając, M.},
journal = {Studia Mathematica},
keywords = {quasinilpotent operator; commutant; reflexivity; quasi-nilpotent operator; reflexive commutant},
language = {eng},
number = {2},
pages = {173-177},
title = {A quasi-nilpotent operator with reflexive commutant, II},
url = {http://eudml.org/doc/216593},
volume = {132},
year = {1999},
}

TY - JOUR
AU - Müller, V.
AU - Zając, M.
TI - A quasi-nilpotent operator with reflexive commutant, II
JO - Studia Mathematica
PY - 1999
VL - 132
IS - 2
SP - 173
EP - 177
AB - A new example of a non-zero quasi-nilpotent operator T with reflexive commutant is presented. The norms $|T^n|$ converge to zero arbitrarily fast.
LA - eng
KW - quasinilpotent operator; commutant; reflexivity; quasi-nilpotent operator; reflexive commutant
UR - http://eudml.org/doc/216593
ER -

References

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  1. [1] Š. Drahovský and M. Zajac, Hyperreflexive operators on finite dimensional Hilbert spaces, Math. Bohem. 118 (1993), 249-254. Zbl0804.47007
  2. [2] D. Hadwin and E. A. Nordgren, Reflexivity and direct sums, Acta Sci. Math. (Szeged) 55 (1991), 181-197. Zbl0780.47032
  3. [3] D. A. Herrero, A dense set of operators with tiny commutants, Trans. Amer. Math. Soc. 327 (1991), 159-183. Zbl0675.41050
  4. [4] W. R. Wogen, On cyclicity of commutants, Integral Equations Operator Theory 5 (1982), 141-143. Zbl0473.47005
  5. [5] M. Zajac, A quasi-nilpotent operator with reflexive commutant, Studia Math. 118 (1996), 277-283. 
  6. [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). 

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