In this short note, we prove that for a dense set A subset of X (X is a Banach space) there is a non-trivial closed subspace M subset of X such that A boolean AND M is dense in M. We use this result to answer a question posed in Madore and Martinez-Avendaiio (2011) [9]. In particular, we show that every hypercyclic operator is subspace-hypercyclic. (C) 2015 Elsevier Inc. All rights reserved.
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