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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Conullity of operators on some $ {\rm 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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DOI: https://doi.org/10.1090/S0002-9939-1970-0261222-7
Keywords: Conullity, proper ideal, Schauder basis, $ FK$-space, $ \beta $-dual
Article copyright: © Copyright 1970 American Mathematical Society