The interplay between algebras and lattices: Stone–Weierstrass for illustration

Positivity - Tập 28 Số 1 - 2024
Sameh Bououn1
1Laboratoire de Recherche LATAO, Département de Mathematiques, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092, El Manar, Tunisia

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer-Verlag, Dordrecht (2006)

Beukers, F., Huisjmans, C.B., de Pagter, B.: Unital embedding and complexification of $$f$$-algebras. Math. Z. 183, 131–144 (1983)

Bonsall, F.F., Duncan, J.: Complete Normed Algebras. Springer-Verlag, Berlin-Heidelberg-New York (1973)

Boulabiar, K.: Some aspects of Riesz multimorphisms. Indag. Math. 13, 419–432 (2002)

Boulabiar, K., Bououn, S.: Truncated vector lattices of bounded real-valued functions, Submitted

Boulabiar, K., Buskes, G., Henriksen, M.: A generalization of a theorem on biseparating maps. J. Math. Ana. Appl. 280, 334–349 (2003)

Boulabiar, K., Hajji, R.: Representation of strongly truncated Riesz spaces. Indag. Math. 31, 741–757 (2020)

Bustamante, J., Arrazola, J.R., Escobedo, R.: $$A$$-realcompact spaces. Revista Mat. Complutense 11, 17–29 (1998)

Fremlin, D.H.: Topological Riesz spaces and Measure Theory. Cambridge Univ. Press, Cambridge (1974)

Garrido, M.I., Jaramillo, J.A.: Variations on the Banach–Stone Theorem. Extrecta Math. 17, 351–383 (2002)

Groenewegen, G.L.M., van Rooij, A.C.M.: Spaces of Continuous Functions. Atlantis Press, Amsterdam (2016)

Huijsmans, C.B., de Pagter, B.: Subalgebras and Riesz subspaces of an $$f$$-algebra. Proc. Lond. Math. Soc. 48, 161–174 (1984)

Kusraev, A.G., Tabuev, S.N.: Multiplicative representation of bilinear operators. Siberian Math. J. 49, 357–366 (2008)

Kriegl, A., Michor, P.W.: The Convenient Setting of Global Analysis. Math. Surveys Mono graphs, vol. 53, Am. Math. Soc., Providence (1997)

Meyer-Neiberg, P.: Banach Lattices. Springer-Verlag, New York-Berlin-Heidelberg (1991)

Pedersen, G.K.: Analysis Now. Springer-Verlag, New York-Berlin-Heidelberg (1989)

Wickstead, A.W.: Banach lattice algebras: some questions, but very few answers. Positivity 21, 803–815 (2017)