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Journal of Operator Theory

Volume 44, Issue 1, Summer 2000  pp. 25-41.

The closure of the unitary orbit of the set of strongly irreducible operators in non-well ordered nest algebra

Authors:  You Qing Ji 1, Chun Lan Jiang 2, and Zong Yao Wang 3
Author institution: 1 Department of Mathematics, Jilin University, Changchun, 130023, P.R. China
2 Dept. of Applied Math. and Physics, Hebei University of Technology, Tianjin, 300103, P.R. China
3 Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, P.R. China


Summary:  A bounded linear operator T on a Hilbert space H is strongly irreducible if T does not commute with any non-trivial idempotent. A nest N is a chain of subspaces of H contain {0} and H, which is closed under intersection and closed span. The nest algebra algN associated with N is the set of all operators which leave each subspace in N invariant. This paper proves that the norm closure of the unitary orbit of the strongly irreducible operators in a nest algebra is the set of operators whose spectrum is connected if and only if N or N are not well-ordered.

Keywords:  Strongly irreducible operator, nest, nest algebra, unitary orbit, spectrum


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