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Separable Banach lattices on which every bounded linear operator is regular

Published online by Cambridge University Press:  09 March 2011

A. W. WICKSTEAD*
Affiliation:
Pure Mathematics Research Centre, Queens University Belfast, Belfast BT7 1NN. e-mail: [email protected]

Abstract

We give a complete description of those separable Banach lattices E with the property that every bounded linear from E into itself is the difference of two positive operators.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2011

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References

REFERENCES

[1]Abramovič, J. A.Some new characterizations of AM-spaces. An. Univ. Craiova Mat. Fiz.-Chim. 6 (1978), 15–26 (Russian). MR601827 (82c:46025).Google Scholar
[2]Abramovič, J. A. and Gejler, V. A.On a question of Fremlin concerning order bounded and regular operators. Colloq. Math. 46 (1982), no. 1, 1517. MR672357 (84b:46008).CrossRefGoogle Scholar
[3]Alfsen, E. M.On the geometry of Choquet simplexes. Math. Scand. 15 (1964), 97110. MR0187141 (32 #4595).CrossRefGoogle Scholar
[4]Alfsen, E. M. Compact Convex Sets and Boundary Integrals (Springer-Verlag, 1971). Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 57. MR0445271 (56 #3615).CrossRefGoogle Scholar
[5]Goullet de Rugy, A.La structure idéale des M-espaces. J. Math. Pures Appl. (9) 51 (1972), 331373 (French). MR0385512 (52 #6373).Google Scholar
[6]Kantorovich, L. V.Concerning the general theory of operations in partially ordered spaces. Dok. Akad. Nauk. SSSR 1 (1936), 271274 (Russian).Google Scholar
[7]Kantorovitch, L. and Vulich, B.Sur la représentation des opérations linéaires. Compositio Math. 5 (1938), 119165 (French). MR1556991.Google Scholar
[8]Meyer-Nieberg, P.Banach Lattices, Universitext. (Springer-Verlag, 1991). MR1128093 (93f:46025).CrossRefGoogle Scholar
[9]Phelps, R. R. Lectures on Choquet's Theorem (D. Van Nostrand Co., Inc., 1966). MR0193470 (33 #1690).Google Scholar
[10]Phelps, R. R.Lectures on Choquet's Theorem. 2nd ed., Lecture Notes in Mathematics, vol. 1757, Springer-Verlag, Berlin, 2001. MR1835574 (2002k:46001).CrossRefGoogle Scholar
[11]Xiong, H. Y.On whether or not for some classical Banach lattices E and F. Nederl. Akad. Wetensch. Indag. Math. 46 (1984), no. 3, 267282, MR763464 (86a:47042).CrossRefGoogle Scholar