# Journal of Operator Theory

Volume 69, Issue 2, Spring 2013 pp. 359-385.

Similarity invariants and compact perturbations of hereditarily indecomposable space operators**Authors**: Chunlan Jiang (1), Yunnan Zhang (2), and Huaijie Zhong (3)

**Author institution:**(1) Mathematics and Information Science College, He bei Normal University, Shijiazhuang, 050016, P.R. China

(2) Mathematics and Information Science College, He bei Normal University, Shijiazhuang, 050016, P.R. China and School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, P.R. China

(3) School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, P.R. China

**Summary:**This paper gives a completely similarity classification of strongly irreducible operators on hereditarily indecomposable spaces by using $K$-theory. And we also prove that every operator with connected spectrum on complex separable hereditarily indecomposable spaces is a small compact perturbation of a strongly irreducible operator.

**Keywords:**Hereditarily indecomposable spaces, strongly irreducible operators, similar invariants, commutant algebras, $K_0$-groups

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