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SPECTRAL RADIUS ALGEBRAS AND C0 CONTRACTIONS. II

Part of: Special classes of linear operators General theory of linear operators

Published online by Cambridge University Press:  22 September 2010

SRDJAN PETROVIC
SRDJAN PETROVIC*
Affiliation:
Department of Mathematics, Western Michigan University, Kalamazoo, MI 49008, USA (email: srdjan.petrovic@wmich.edu)
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Abstract

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We consider spectral radius algebras associated with C0 contractions. When the operator A is algebraic, we describe all invariant subspaces that are common for operators in its spectral radius algebra ℬA. When the operator A is not algebraic, ℬA is weakly dense and we characterize a set of rank-one operators in ℬA that is weakly dense in ℒ(ℋ).

Keywords

spectral radius algebrasinvariant subspacesC0 contractionJordan block

MSC classification

Secondary: 47A15: Invariant subspaces 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 1 , August 2010 , pp. 91 - 104
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

References

[1]Bercovici, H., Operator Theory and Arithmetic in H ∞ (American Mathematical Society, Providence, RI, 1988).CrossRefGoogle Scholar
[2]Biswas, A., Lambert, A. and Petrovic, S., ‘Extended eigenvalues and the Volterra operator’, Glasg. Math. J. 44(3) (2002), 521–534.CrossRefGoogle Scholar
[3]Biswas, A., Lambert, A. and Petrovic, S., ‘On spectral radius algebras and normal operators’, Indiana Univ. Math. J. 4 (2007), 1661–1674.CrossRefGoogle Scholar
[4]Biswas, A., Lambert, A., Petrovic, S. and Weinstock, B., ‘On spectral radius algebras’, Oper. Matrices 2(2) (2008), 167–176.CrossRefGoogle Scholar
[5]Biswas, A. and Petrovic, S., ‘On extended eigenvalues of operators’, Integral Equations Operator Theory 55(2) (2006), 233–248.CrossRefGoogle Scholar
[6]Lambert, A. and Petrovic, S., ‘Beyond hyperinvariance for compact operators’, J. Funct. Anal. 219(1) (2005), 93–108.CrossRefGoogle Scholar
[7]Petrovic, S., ‘On the extended eigenvalues of some Volterra operators’, Integral Equations Operator Theory 57(4) (2007), 593–598.CrossRefGoogle Scholar
[8]Petrovic, S., ‘On the structure of the spectral radius algebras’, J. Operator Theory 60(1) (2008), 137–148.Google Scholar
[9]Petrovic, S., ‘Spectral radius algebras and C 0 contractions’, Proc. Amer. Math. Soc. 136 (2008), 4283–4288.CrossRefGoogle Scholar
[10]Radjavi, H. and Rosenthal, P., Invariant Subspaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 77 (Springer, Berlin and New York, 1973).CrossRefGoogle Scholar