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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On projections in power series spaces and the existence of bases


Author: Jörg Krone
Journal: Proc. Amer. Math. Soc. 105 (1989), 350-355
MSC: Primary 46A45; Secondary 46A35
MathSciNet review: 933516
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Abstract: Mityagin posed the problem, whether complemented subspaces of nuclear infinite type power series spaces have a basis. A related more general question was asked by Pełczyński. It is well known for a complemented subspace $ E$ of a nuclear infinite type power series space, that its diametral dimension can be represented by $ \Delta E = \Delta {\Lambda _\infty }(\alpha )$ for a suitable sequence $ \alpha $ with $ {\alpha _j} \geq \ln (j + 1)$. In this article we prove the existence of a basis for $ E$ in case that $ {\alpha _j} \geq j$ and $ \sup \tfrac{{{\alpha _{2j}}}}{{{\alpha _j}}} < \infty $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0933516-5
PII: S 0002-9939(1989)0933516-5
Article copyright: © Copyright 1989 American Mathematical Society