On weak bases in functional spaces

V. P. Kondakov<sup>ab

a</sup> Southern Federal University, RUSSIA, Rostov-on-Don
^b South Mathematical Institute of VSC RAS, RUSSIA, Vladikavkaz

Abstract: For a strictly webbed Montel space $E$ with complete separable $E'_\beta$ (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.

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

UDC: 513.881

Received: 01.03.2010

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