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Remarks on Bases in a Fréchet Function Space
Päivi MATTILA and Jari TASKINEN
University of Helsinki
Department of Mathematics
Hallituskatu 15
SF-00100 Helsinki — Finland

Received: August 28, 1992
Revised: December 10, 1992
ABSTRACT

We present an explicit construction of a Schauder basis in the space C(R) /~\ Lp(R) for all p , 1< p< oo . This basis cannot be unconditional, since we give a proof of the fact that the Banach spaces C(0,1) or L1(0,1) cannot be embedded in a Fréchet space with an unconditional basis.

1991 Mathematics Subject Classification: 46A06, 46E10.