Abstract
In this note the existence of an operator extending linear functionals from a subspace to the whole space is studied. It is shown that under certain conditions on the Banach lattice of measurable functions and on a suitable subspace, there exists a unique extension operator.
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Literature cited
B. S. Mityagin and G. M. Khenkin, “Linear problems in complex analysis,” Usp. Mat. Nauk,26, No. 4, 93–152 (1971).
E. M. Semenov, “Imbedding theorems for Banach spaces of measurable functions,” Dokl. Akad. Nauk SSSR,157, No. 6, 1292–1295 (1964).
B. Z. Vulikh, Introduction to the Theory of Semiordered Spaces [in Russian], Fizmatgiz, Moscow (1961).
Additional information
Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 733–739, November, 1976.
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Braverman, M.S., Lozanovskii, G.Y. Extension of linear functionals in Banach spaces of measurable functions. Mathematical Notes of the Academy of Sciences of the USSR 20, 969–973 (1976). https://doi.org/10.1007/BF01146921
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DOI: https://doi.org/10.1007/BF01146921