A formula for the joint local spectral radius

Authors:
E. Yu. Emel'yanov and Z. Ercan

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1449-1451

MSC (2000):
Primary 47A11, 47A13, 46H05

DOI:
https://doi.org/10.1090/S0002-9939-03-07199-5

Published electronically:
October 8, 2003

MathSciNet review:
2053352

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a formula for the joint local spectral radius of a bounded subset of bounded linear operators on a Banach space in terms of the dual of .

**[1]**J. Diestel,*Sequences and series in Banach spaces,*Graduate Texts in Mathematics**92**, Springer-Verlag, New York (1984). MR**85i:46020****[2]**R. Drnovsek,*On reducibility of semigroups of compact quasinilpotent operators,*Proc. Amer. Math. Soc.**125**(1997), 2391-2394. MR**97m:47007****[3]**Z. Ercan and S. Onal,*Invariant subspaces for positive operators acting on a Banach space with Markuhevich basis,*Positivity. (to appear)**[4]**P. Rosenthal and A. Soltysiak,*Formulas for the joint spectral radius of noncommuting Banach algebra elements,*Proc. Amer. Math. Soc.**123**(1995), 2705-2708. MR**95k:47008****[5]**G.-C. Rota and W. G. Strang,*A note on the joint spectral radius,*Indag. Math.**22**(1960), 379-381. MR**26:5434****[6]**V. S. Shulman and Yu. V. Turovskii,*Joint spectral radius, operator semigroups, and a problem of W. Wojtynski,*J. Funct. Anal.**177**(2000), 383-441. MR**2002d:47099**

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Additional Information

**E. Yu. Emel'yanov**

Affiliation:
Sobolev Institute of Mathematics, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia

Address at time of publication:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey

Email:
emelanov@math.nsc.ru

**Z. Ercan**

Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey

Email:
zercan@metu.edu.tr

DOI:
https://doi.org/10.1090/S0002-9939-03-07199-5

Keywords:
Joint local spectral radius,
joint spectral radius,
Banach algebra

Received by editor(s):
November 23, 2002

Received by editor(s) in revised form:
January 9, 2003

Published electronically:
October 8, 2003

Additional Notes:
The work of the first author was supported by the Scientific and Technical Research Council of Turkey

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2003
American Mathematical Society