Conullity of operators on some -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) -space and the following question is studied: Given a subalgebra of the algebra of all continuous linear operators on this -space, is there a class of operators in this subalgebra whose behavior is ``conull-like"? The question is answered in the case when the -space has a suitable (Schauder) basis and also in some other special cases.

**[1]**H. I. Brown, D. R. Kerr and H. H. Stratton,*The structure of**and extensions of the concept of conull matrix*, Proc. Amer. Math. Soc.**22**(1969), 7-14. MR**0304931 (46:4062)****[2]**J. J. Sember,*A note on conull**spaces and variation matrices*, Math. Z.**108**(1968), 1-6. MR**0273376 (42:8255)****[3]**A. K. Snyder,*Conull and coregular**spaces*, Math. Z.**90**(1965), 376-381. MR**32**#2783. MR**0185315 (32:2783)****[4]**A. Wilansky,*Functional analysis*, Blaisdell, Waltham, Mass., 1964. MR**30**#425. MR**0170186 (30:425)****[5]**-,*Topics in functional analysis*, Lecture Notes in Math., no. 45, Springer-Verlag, Berlin and New York, 1967. MR**36**#6901. MR**0223854 (36:6901)****[6]**-,*Topological divisors of zero and Tauberian theorems*, Trans. Amer. Math. Soc.**113**(1964), 240-251. MR**29**#6222. MR**0168967 (29:6222)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1970-0261222-7

Keywords:
Conullity,
proper ideal,
Schauder basis,
-space,
-dual

Article copyright:
© Copyright 1970
American Mathematical Society