Abstract
In 1941 Nakano gave a characterisation of real spaces C0(Σ) as M-spaces satisfying an additional restriction on their norm. We give an isomorphic version of Nakano’s result which involves showing that for any Banach lattice (a suitably modified version of) Nakano’s condition is equivalent to the norm on the Dedekind completion being Fatou.
Similar content being viewed by others
References
Y.A. Abramovich, C.D. Aliprantis, An Invitation to Operator Theory. American Mathematical Society (Graduate Studies in Mathematics 50), Providence, Rhode Island (2002).
E.M. Alfsen, Compact Convex Sets and Boundary Integrals. Springer-Verlag, New York (1971).
P. Meyer-Nieberg, Banach Lattices. Springer-Verlag, Berlin-Heidelberg (1991).
H. Nakano, Über die Charakterisierung des allgemeinen C-Raumes, Proc. Imp. Acac. Tokyo, 17 (1941) 301–307.
H. Nakano, Über normierte teilweisegeordnete Moduln, Proc. Imp. Acac. Tokyo, 17 (1941) 311–317.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wickstead, A.W. An Isomorphic Version of Nakano’s Characterisation of C0(Σ). Positivity 11, 609–615 (2007). https://doi.org/10.1007/s11117-007-2078-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11117-007-2078-6