# Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

Studia Mathematica (1999)

- Volume: 134, Issue: 2, page 153-167
- ISSN: 0039-3223

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topLyubich, Yu.. "Spectral localization, power boundedness and invariant subspaces under Ritt's type condition." Studia Mathematica 134.2 (1999): 153-167. <http://eudml.org/doc/216629>.

@article{Lyubich1999,

author = {Lyubich, Yu.},

journal = {Studia Mathematica},

keywords = {power bounded operator; Nevanlinna's theorem; Katznelson-Tzafriri theorem},

language = {eng},

number = {2},

pages = {153-167},

title = {Spectral localization, power boundedness and invariant subspaces under Ritt's type condition},

url = {http://eudml.org/doc/216629},

volume = {134},

year = {1999},

}

TY - JOUR

AU - Lyubich, Yu.

TI - Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

JO - Studia Mathematica

PY - 1999

VL - 134

IS - 2

SP - 153

EP - 167

LA - eng

KW - power bounded operator; Nevanlinna's theorem; Katznelson-Tzafriri theorem

UR - http://eudml.org/doc/216629

ER -

## References

top- [1] K. Hoffman, Banach Spaces of Analytic Functions, Prentice-Hall, 1962. Zbl0117.34001
- [2] Y. Katznelson and L. Tzafriri, On power bounded operators, J. Funct. Anal. 68 (1986), 313-328. Zbl0611.47005
- [3] Yu. Lyubich and V. Matsaev, Operators with separable spectrum, in: Amer. Math. Soc. Transl. (2) 47 (1965), 89-129. Zbl0158.14602
- [4] B. Nagy and J. Zemánek, A resolvent condition implying power boundedness, Studia Math. 134 (1999), 143-151. Zbl0934.47002
- [5] O. Nevanlinna, Convergence of Iterations for Linear Equations, Birkhäuser, 1993.
- [6] R. K. Ritt, A condition that $li{m}_{n\to \infty}{n}^{-1}{T}^{n}=0$, Proc. Amer. Math. Soc. 4 (1953), 898-899. Zbl0052.12501
- [7] J. G. Stampfli, A local spectral theory for operators IV; Invariant subspaces, Indiana Univ. Math. J. 22 (1972), 159-167. Zbl0254.47007
- [8] E. Tadmor, The resolvent condition and uniform power boundedness, Linear Algebra Appl. 80 (1986), 250-252.

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