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Incompleteness of the linear span of the positive compact operators

Author(s): Z. L. Chen; A. W. Wickstead
Journal: Proc. Amer. Math. Soc. 125 (1997), 3381-3389.
MSC (1991): Primary 47B65; Secondary 47B07
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Abstract: We show that even in the case of a Banach lattice $E$ with an order continuous norm (or whose dual has an order continuous norm) the linear span of the positive compact operators on $E$ need not be complete under the regular norm.

References:

[1]
Y. A. Abramovich and A. W. Wickstead, A compact regular operator without modulus, Proc. Amer. Math. Soc. 116 (1992), 721-726. MR 93a:47038

[2]
Y.A. Abramovich and A.W. Wickstead, Recent results on the order structure of compact operators, Irish Math. Soc. Bulletin 32 (1994), 32-45. MR 95h:47050

[3]
Y. A. Abramovich and A. W. Wickstead, Solutions of several problems in the theory of compact positive operators, Proc. Amer. Math. Soc. 123 (1995), 3021-3026. MR 95m:47059

[4]
C. D. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York & London, 1985. MR 87h:47086

[5]
W. Arendt, On the o-spectrum of regular operators and the spectrum of measures, Math.Z. 178 (1981), 271-287. MR 83h:47027

[6]
W. Arendt and A.R. Sourour, Ideals of regular operators on $\ell ^{2}$, Proc. Amer. Math. Soc. 88 (1983), 93-96. MR 84c:47048

[7]
W. Arendt and A.R. Sourour, Perturbation of regular operators and the order essential spectrum, Indag. Math. 48 (1986), 109-122. MR 87j:47052

[8]
P.G. Dodds and D.H. Fremlin, Compact operators in Banach lattices, Israel J. Maths. 34 (1979), 287-320. MR 81g:47037

[9]
U. Krengel, Über den Absolutbetrag stetiger linearer Operatoren und seine Anwendung auf ergodische Zerlegungen, Math. Scand. 13 (1963), 151-187. MR 31:310

[10]
U. Krengel, Remark on the modulus of compact operators, Bull. Amer. Math. Soc. 72 (1966), 132-133. MR 32:8162

[11]
P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin Heidelberg New York, 1991. MR 93f:46025

[12]
H. Raubenheimer, The $o$-spectrum of $r$-asymptotically quasi-finite rank operators, Quaest. Math. 7 (1984), 299-303. MR 86c:47050

[13]
H. Raubenheimer, $R$-asymptotically quasi-finite rank operators and the spectrum of measures,, Quaest. Math. 10 (1986), 97-111. MR 87m:47090

[14]
A.W. Wickstead, Spaces of operators with the Riesz separation property, Indag. Math. N.S. 6 (1995), 235-245. MR 96g:47032

[15]
A.W. Wickstead, Converses for the Dodds-Fremlin and Kalton-Saab theorems, Math. Proc. Camb. Phil. Soc. 120 (1996), 175-179. MR 96m:47067

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Additional Information:

Z. L. Chen
Affiliation: Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland

A. W. Wickstead
Affiliation: Department of Pure Mathematics, The Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland
Email: A.Wickstead@qub.ac.uk

DOI: 10.1090/S0002-9939-97-04220-2
PII: S 0002-9939(97)04220-2
Keywords: Compact operators, regular operators
Received by editor(s): June 26, 1996
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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