A quasi-nilpotent operator with reflexive commutant, II

• Autorzy: V. Müller , M. Zając
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

quasinilpotent operator; commutant; reflexivity

Kategorie tematyczne

• 47A15: Invariant subspaces
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 132
• Numer: 2
• Strony: 173-177

Daty

wydano

1999

otrzymano

1998-03-31

Twórcy

autor

V. Müller

• Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic

autor

M. Zając

• epartment of Mathematics, Faculty of Electrical Engineering, Slovak University of Technology, Ilkovičova 3, 812 19 Bratislava, Slovak Republic

Bibliografia

• [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).