Let A be an invertible bounded linear operator on a complex Banach space, {A}�� the commutant of A and BA the set of all operators T such that supn.0 �aAnTA .n�a < +��.
Equality {A}�� = BA was studied by many authors for differents classes of operators. In this paper we investigate a local version of this equality and the case where A is a C0.contraction.
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