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The Riesz decomposition property for the space of regular operators

Author(s): Nicolae Danet
Journal: Proc. Amer. Math. Soc. 129 (2001), 539-542.
MSC (1991): Primary 47B60; Secondary 47B65, 46B42, 47L05
Posted: September 20, 2000
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Abstract:

If $E$ and $F$ are Banach lattices such that $E$ is separable and $F$ has the countable interpolation property, then the space of all continuous regular operators $\mathcal{L}$$^r(E,F)$ has the Riesz decomposition property. This result is a positive answer to a conjecture posed by A. W. Wickstead.

References:

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Y. A. Abramovich and A. W. Wickstead, Regular operators from and into a small Riesz space, Indag. Mathem., N.S. 2 (1991), no.3, 257-274. MR 93i:47052

2.
Y. A. Abramovich and A. W. Wickstead, The regularity of order bounded operators into C(K), II, Quart. J. Math. Oxford (2), 44 (1993), 257-270. MR 94h:47067

3.
C. B. Huijsmans and B. de Pagter, On z-ideals and d-ideals in Riesz spaces, II, Indag. Mathem. 42 (1980), no.4, 391-408. MR 83c:46004a

4.
Peter Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin Heidelberg New York, 1991. MR 93f:46025

5.
G. L. Seever, Measures on F-spaces, Trans. Amer. Math. Soc.133 (1968), 267-280. MR 37:1976

6.
A. W. Wickstead, Spaces of operators with the Riesz separation property, Indag. Mathem., N.S. 6 (1995), no.2, 235-245. MR 96g:47032

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Additional Information:

Nicolae Danet
Affiliation: Technical University of Civil Engineering of Bucharest, 122-124, Lacul Tei Blvd., 72302 Bucharest, Romania
Email: ndanet@fx.ro

DOI: 10.1090/S0002-9939-00-05592-1
PII: S 0002-9939(00)05592-1
Keywords: Banach lattices, regular operators, Riesz decomposition property
Received by editor(s): December 17, 1998
Received by editor(s) in revised form: May 4, 1999
Posted: September 20, 2000
Dedicated: Dedicated to Prof. Romulus Cristescu on his 70th birthday
Communicated by: David R. Larson
Copyright of article: Copyright 2000, American Mathematical Society

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