On weak bases in functional spaces

Kondakov V. P.
Vladikavkaz Mathematical Journal 2011. Vol. 13. Issue 1.

Abstract:
For a strictly webbed Montel space  \(E\) with complete separable \(E_\beta^\prime\) (strong dual of \(E\)), we show that a weak bases in \(E\) is  Schauder basis with equicontinuons coefficientive functionals. This result is  applied to bases in spaces  of holomorphic functions. In particular,  from it the absolutenes of all bases in some classes of nonmetrizable nuclear functional spaces follows.

Keywords: weak bases, Schauder bases, Montel spaces, spaces of infinite-dimensional holomorphy.

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