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$%P. Mattila and J. Taskinen, Remarks on bases in a Fréchet function space, Rev. Mat. Univ. Complut. Madrid 6 (1993), no. 1, 8399.%$

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.