Conullity of operators on some 𝐹𝐾-spaces

Brown, H. I.; Stratton, H. H.

doi:10.1090/S0002-9939-1970-0261222-7

Conullity of operators on some $\textrm {FK}$-spaces

Authors: H. I. Brown and H. H. Stratton
Journal: Proc. Amer. Math. Soc. 25 (1970), 717-727
MSC: Primary 40.50
DOI: https://doi.org/10.1090/S0002-9939-1970-0261222-7
MathSciNet review: 0261222
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Abstract: The notion of conullity for a subclass of the algebra of matrix operators on the space of convergent sequences is well known in summability theory. In this paper the space of convergent sequences is replaced by a general (locally convex) $FK$-space and the following question is studied: Given a subalgebra of the algebra of all continuous linear operators on this $FK$-space, is there a class of operators in this subalgebra whose behavior is “conull-like"? The question is answered in the case when the $FK$-space has a suitable (Schauder) basis and also in some other special cases.

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