Strongly irreducible operators and Cowen-Douglas operators on c ₀, l _p (1 ⩽ p < ∞)

Abstract

This paper gives some sufficient conditions for the strongly irreducibility of operators which have the forms of upper triangular operator matrices on Banach spaces. Based on these results, strongly irreducible Cowen-Douglas operators of index n are constructed on c ₀, l _p (1 ⩽ p < ∞) for all 1 ⩽ n ⩽ ∞.

Keywords

Banach space / strongly irreducible operator / Cowen-Douglas operator / upper triangular operator matrice

References

[1] Cao Y., Fang J. S., Jiang C. L. K-groups of Banach algebras and strongly irreducible decompositions of operators. J Operator Theory, 2002, 48, 235-253

[2] Cowen M. J., Douglas R. G. Complex geometry and operator theory. Acta Math, 1978, 141, 187-261

[3] Davis C., Rosenthal P. Solving linear operator equations. Canad J Math, 1974, 26, 1384-1389

[4] Gilfeather F. Strongly irreducibility of operators. Indiana Univ Math J, 1972, 22, 97-133

[5] Herrero D. A. An essay on quasisimilarity. Special Classes of Linear Operators and other Topics, Eleventh International Conference on Operator Theory, Bucharest (Romania), June, 1986. OT: Advances and Applications, 28, 1988, Basel: Birkhäuser-Verlag 125-154

[6] Herrero D. A., Jiang C. L. Limits of strongly irreducible operators and the Riesz decomposition theorem. Mich Math J, 1990, 37, 283-291

[7] Ji Y. Q., Jiang C. L. Small compact perturbation of strongly irreducible operators. Integr Equ Oper Theory, 2002, 43, 417-449

[8] Jiang C. L. Strongly irreducibility operators and Cowen-Douglas operators. Northeast Math J, 1991, 7, 1-3

[9] Jiang C. L. Similarity reducibility and approximation of Cowen-Douglas operators. J Operator Theory, 1994, 32, 77-89

[10] Jiang C. L. Similarity classification of Cowen-Douglas operators. Canad J Math, 2004, 56, 742-775

[11] Jiang C. L., Guo X. Z., Ji K. K-group and similarity classification of operators. J Funct Anal, 2005, 225, 167-192

[12] Jiang C. L., He H. Quasisimilarity of Cowen-Douglas operators. Science in China, Ser A, 2004, 47, 297-310

[13] Jiang C. L., Ji K. Similarity classification of holomorphic curves. Adv Math, 2007, 215, 446-468

[14] Jiang C. L., Li J. X. The irreducible decomposition of Cowen-Douglas operators and operator weighted shifts. Acta Sci Math, 2000, 66, 679-695

[15] Jiang C. L., Wang Z. Y. Strongly Irreducibility Operators on Hilbert Space, 1998, Harlow: Longman.

[16] Jiang C. L., Wang Z. Y. Structure of Hilbert Space Operators, 2006, Singapore: World Scientific