A note on the powers of Cesàro bounded operators

Zoltán Léka

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 4, page 1091-1100
  • ISSN: 0011-4642

Abstract

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In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator T on a Hilbert space with a single spectrum satisfies lim n → ∞ ∥ T n + 1 - T n ∥ = 0 .

How to cite

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Léka, Zoltán. "A note on the powers of Cesàro bounded operators." Czechoslovak Mathematical Journal 60.4 (2010): 1091-1100. <http://eudml.org/doc/196551>.

@article{Léka2010,
abstract = {In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator $T$ on a Hilbert space with a single spectrum satisfies $\lim _\{n \rightarrow \infty \} \Vert T^\{n+1\} - T^n\Vert = 0.$},
author = {Léka, Zoltán},
journal = {Czechoslovak Mathematical Journal},
keywords = {Volterra operator; stability of operators; Volterra operator; stability of operators},
language = {eng},
number = {4},
pages = {1091-1100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the powers of Cesàro bounded operators},
url = {http://eudml.org/doc/196551},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Léka, Zoltán
TI - A note on the powers of Cesàro bounded operators
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 4
SP - 1091
EP - 1100
AB - In this note we give a negative answer to Zem�nek’s question (1994) of whether it always holds that a Cesàro bounded operator $T$ on a Hilbert space with a single spectrum satisfies $\lim _{n \rightarrow \infty } \Vert T^{n+1} - T^n\Vert = 0.$
LA - eng
KW - Volterra operator; stability of operators; Volterra operator; stability of operators
UR - http://eudml.org/doc/196551
ER -

References

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  10. Szegö, G., Orthogonal Polynomials, 4th ed. Amer. Math. Soc. Colloq. Publ., Vol. 23, Amer. Math. Soc. Providence (1975). (1975) MR0310533
  11. Tomilov, Y., Zem�nek, J., 10.1017/S0305004103007436, Math. Proc. Camb. Philos. Soc. 137 (2004), 209-225. (2004) MR2075049DOI10.1017/S0305004103007436
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