Abstract
The paper deals with an analytic characterization of unconditional bases, a characterization of the unconditional character of a Schauder base for the associated cone and a number of counterexamples supporting various conditions appearing in the theorems.
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References
L. H. Carter, An order topology in ordered topological vector spaces,Trans. Amer. Math. Soc. 216 (1976), 131–144.MR 52: 11527
M. M. Day,Normed linear spaces, Springer, Berlin, 1973.MR 49: 9588
E. L. Dubinsky andJ. R. Retherford, Schauder bases and Köthe sequence spaces,Trans. Amer. Math. Soc. 130 (1968), 265–280.MR 38: 510
J. Horváth,Topological vector spaces and distributions, I, Addison-Wesley, Reading (Mass.), 1966.MR 34: 4863
P. K. Kamthan andM. Gupta,Theory of bases and cones, Pitman, London, 1985.
P. K. Kamthan andM. Gupta,Sequence spaces and series, Dekker, New York, 1981.MR 83g: 46011
G. Köthe,Topological vector spaces, I, Springer, Berlin, 1969.MR 24A: 411;33: 3069;40: 1750
C. W. McArthur, Convergence of monotone nets in ordered topological vector spaces,Studia Math. 34 (1970), 1–16.MR 41: 4197
C. W. McArthur, Developments in Schauder basis theory,Bull. Amer. Math. Soc. 78 (1972), 877–908.MR 47: 2320
C. W. McArthur, I. Singer andM. Levin, On the cones associated with biorthogonal systems and bases in Banach spaces,Canad. J. Math. 21 (1969), 1206–1217.MR 41: 4207
A. L. Peressini,Ordered topological vector spaces, Harper & Row, New York, 1967.MR 37: 3315
W. H. Ruckle,Sequence spaces, Pitman, Boston, 1981.MR 83g: 46012
I. Singer,Bases in Banach spaces, I, Springer, New York, 1970.MR 45: 7451
L. J. Weill, Unconditional and shrinking bases in locally convex spaces,Pacific J. Math. 29 (1969), 467–483.MR 39: 7389
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Gupta, M., Kamthan, P.K. Unconditional bases and the order structure. Period Math Hung 17, 279–294 (1986). https://doi.org/10.1007/BF01848389
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DOI: https://doi.org/10.1007/BF01848389