Abstract
In this paper, we first give some invariant subspace results for collectively compact sets of operators in connection with the joint spectral radius of these sets. We then prove that any collectively compact set M in algΓ satisfies Berger-Wang formula, where Γ is a complete chain of subspaces of X.
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References
Y.A. Abramovich, C.D. Aliprantis, An invitation to operator theory. Graduate Stud Math., 50, Amer. Math. Soc. (2002).
P.M. Anselone, Collectively Compact Operator Approximation Theory and Applications to Integral Equations , Prentice-Hall Inc. (1971).
M.A. Berger, Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166 (1992), 21–27.
H. Radjavi, P. Rosenthal, Simultaneous Triangularization, Springer (2000).
P. Rosenthal, A. Soltysiak, Formulas for the joint spectral radius of non-commuting Banach algebra elements, Proc. Am. Math. Soc. 123 (9) (1995), 2705–2708.
G.C. Rota, W.G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379–381.
V.S. Shulman, Yu.V. Turovskii, Joint spectral radius, operator semigroups and a problem of W.Wojtynski . J. Funct. Anal. 177 (2000), 383–441.
Yu.V. Turovskii, Volterra semigroups have invariant subspaces, J. Funct. Anal. 162 (1999), 313–322.
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Alpay, Ş., Mısırlıoğlu, T. Invariant Subspaces of Collectively Compact Sets of Linear Operators. Positivity 12, 209–219 (2008). https://doi.org/10.1007/s11117-007-2089-3
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DOI: https://doi.org/10.1007/s11117-007-2089-3