Date: 03 Aug 2011

A note on J-sets of linear operators

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Abstract

We construct a Banach space operator \({T \in B(X)}\) such that the set J T (0) has a nonempty interior but J T (0) ≠ X. This gives a negative answer to a problem raised by Costakis and Manoussos (J. Oper. Theory [in press], 2011).

The research was supported by grants 201/09/0473 of GA ČR, IAA100190903 of GA AV and Institution Research Plan AV OZ 10190503.