On local spectral properties of complex symmetric operators

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Abstract

In this paper we study properties of complex symmetric operators. In particular, we prove that every complex symmetric operator having property (β) or (δ) is decomposable. Moreover, we show that complex symmetric operator T has Dunfordʼs property (C) and it satisfies Weylʼs theorem if and only if its adjoint does.

Keywords

Complex symmetric operator
Dunfordʼs property (C)
Property (β)
Decomposable
Invariant subspaces
Weylʼs theorem

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This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korean Government (MEST) (2009-0093125). The forth author was supported by the National Research Foundation of Korea grant funded by the Korean Government (Ministry of Education, Science and Technology) [KRF-2010-355-C00005].