The Brezis–Lieb lemma in convergence vector lattices

Recently measure-free versions of the Brezis–Lieb lemma were proved for unbounded order convergence invector lattices. In this article, we extend these versions to convergence vector lattices.

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[1] Aliprantis CD, Burkinshaw O. Positive Operators. Dordrecht, the Netherlands: Springer, 2006.
[2] Anguelov R, van der Walt JH. Order convergence structure on C(X). Quaest Math 2005; 28: 425-457.
[3] Beattie R, Butzmann HP. Convergence Structures and Applications to Functional Analysis. Dordrecht, the Netherlands: Springer-Science+Business Media, B.V., 2002.
[4] Brezis H, Lieb E. A relation between pointwise convergence of functions and convergence of functionals. P Am Math Soc 1983; 88: 486-490.
[5] Brezis H, Nirenberg L. Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Commun Pur Appl Math 1983; 36: 437-477.
[6] Dabboorasad YA, Emelyanov EY, Marabeh MAA. uτ -Convergence in locally solid vector lattices. preprint 2017; arXiv:1706.02006v3 [math.FA].
[7] Emelyanov EY, Marabeh MAA. Two measure-free versions of the Brezis-Lieb Lemma. Vladikavkaz Mat Zh 2016; 18: 21-25.
[8] Gao N, Xanthos F. Unbounded order convergence and application to martingales without probability. J Math Anal Appl 2014; 415: 931-947.
[9] Lieb E. Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities. Ann Math 1983; 118: 349-374.
[10] Luxemburg WAJ, Zaanen AC. Riesz Spaces, Volume I. Amsterdam, the Netherlands: North-Holland Publishing Company, 1971.
[11] Schaefer HH. Banach Lattices and Positive Operators. Berlin, Germany: Springer-Verlag, 1974.
[12] van der Walt JH. The order convergence structure. Indagat Math New Ser 2011; 21: 138-155.
[13] van der Walt JH. Applications of convergence spaces to vector lattice theory. Topol P 2014; 41: 311-331.
[14] Zaanen AC. Riesz Spaces II. Amsterdam, the Netherlands: North-Holland Publishing Company, 1983.

ISSN: 1300-0098
Yayın Aralığı: Yılda 6 Sayı
Yayıncı: TÜBİTAK

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