We consider the well-known problem: when does an analogue of von Neumann Double Commutant Theorem hold for a multiplication operator on a Banach space of functions? We get an affirmative answer to the above problem for multiplication operators on C(K), where K is a locally connected continuum. In the second part of the paper we solve the above mentioned problem for multiplication operators on C (1)[0, 1] in the case when the multiplier is either a polynomial or a non-decreasing function.
Positivity – Springer Journals
Published: Jul 13, 2010
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