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 | References | Similar Articles | Additional Information
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 βconull-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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- Albert Wilansky, Functional analysis, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1964. MR 0170186
- Albert Wilansky, Topics in functional analysis, Lecture Notes in Mathematics, No. 45, Springer-Verlag, Berlin-New York, 1967. Notes by W. D. Laverell. MR 0223854
- Albert Wilansky, Topological divisors of zero and Tauberian theorems, Trans. Amer. Math. Soc. 113 (1964), 240β251. MR 168967, DOI https://doi.org/10.1090/S0002-9947-1964-0168967-X
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Additional Information
Keywords:
Conullity,
proper ideal,
Schauder basis,
<IMG WIDTH="40" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img9.gif" ALT="$FK$">-space,
<IMG WIDTH="18" HEIGHT="39" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$\beta$">-dual
Article copyright:
© Copyright 1970
American Mathematical Society