On projections in power series spaces and the existence of bases
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- by Jörg Krone PDF
- Proc. Amer. Math. Soc. 105 (1989), 350-355 Request permission
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 $\sup \tfrac {{{\alpha _{2j}}}}{{{\alpha _j}}} < \infty$.References
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Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 350-355
- MSC: Primary 46A45; Secondary 46A35
- DOI: https://doi.org/10.1090/S0002-9939-1989-0933516-5
- MathSciNet review: 933516