On the multiplicative completion of centered systems

In their consideration of the completeness phenomenon in L2(a, b), Boas and Pollard have shown that a cofinite subset of a complete system can be transformed into a complete system by multiplying each member of the system by a fixed, bounded measurable function. Following a trail blazed by Braun and extensively developed by Kazarian, one can show that some systems, complete in Lp(E), can be transformed, à la Boas and Pollard, in such a manner that the new system is, in fact, a quasibasis for Lp(E). Here it is shown that certain families of centered functions can be transformed in this manner.  2003 Elsevier Inc. All rights reserved.