A. K. Dronov, V. M. Kaplitskii, “On the existence of a basis in a complemented subspace of a nuclear Köthe space from class <nobr>$(d_1)$</nobr>”, Mat. Sb., 2018, Volume 209, Number 10,Pages <nobr>50

This article is cited in 2 papers

On the existence of a basis in a complemented subspace of a nuclear Köthe space from class $(d_1)$

A. K. Dronov^a, V. M. Kaplitskii^bc

^a Rostov State University of Economics, Rostov-on-Don
^b Southern Federal University, Rostov-on-Don
^c Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: A proof is presented that an arbitrary complemented subspace of a Köthe nuclear space from class $(d_1)$ has a basis, provided that the relevant Köthe matrix is regular in the sense of Dragilev. It is also shown that each such subspace must have a basis that is quasi-equivalent to a part of the canonical unit-vector basis.
Bibliography: 21 titles.

Keywords: basis, Köthe nuclear spaces, Pelczyński's conjecture, complemented subspaces.

UDC: 517.98+517.982.254

MSC: Primary 46A35, 46A45; Secondary 46B70

Received: 15.10.2016 and 03.11.2017

DOI: 10.4213/sm8843