Order and geometric properties of the set of Banach limits

E. A. Alekhno ; E. M. Semenov ; F. A. Sukochev ; A. S. Usachev

Algebra i analiz, Tome 28 (2016) no. 3, pp. 3-35.

Bibliographie

[1] Alekhno E. A., “Nekotorye spetsialnye svoistva funktsionalov Mazura. II”, Tr. Mezhdunar. konf. AMADE-2006, v. 2, Minsk, 2006, 17–23

[2] Alekhno E. A., “Superposition operator on the space of sequences almost converging to zero”, Cent. Eur. J. Math., 10:2 (2012), 619–645 | DOI | MR | Zbl

[3] Alekhno E. A., “On Banach–Mazur limits”, Indag. Math. (N.S.), 26:4 (2015), 581–614 | DOI | MR | Zbl

[4] Alekhno E. A., Semenov E. M., Sukochev F. A., Usachev A. S., “Poryadkovye svoistva mnozhestva banakhovykh predelov”, Dokl. RAN, 460:2 (2015), 131–132 | DOI | MR | Zbl

[5] Aliprantis C. D., Border K. C., Infinite dimensional analysis. A hitchhiker's guide, Springer-Verlag, Berlin, 2006 | MR | Zbl

[6] Aliprantis C. D., Burkinshaw O., Positive operators, Pure Appl. Math., 119, Acad. Press, Orlando, FL, 1985 | MR | Zbl

[7] Aliprantis C. D., Burkinshaw O., Locally solid Riesz spaces with applications to economics, Math. Surveys Monogr., 105, Amer. Math. Soc., Providence, RI, 2003 | DOI | MR | Zbl

[8] Banakh S., Teoriya lineinykh operatsii, RKhD, Moskva–Izhevsk, 2001

[9] Jerison M., “The set of all generalized limits of bounded sequences”, Canad. J. Math., 9:1 (1957), 79–89 | DOI | MR | Zbl

[10] Dodds P. G., de Pagter B., Sedaev A. A., Semenov E. M., Sukochev F. A., “Singulyarnye simmetrichnye funktsionaly i banakhovy predely s dopolnitelnymi svoistvami invariantnosti”, Izv. RAN. Ser. mat., 67:6 (2003), 111–136 | DOI | MR | Zbl

[11] Carothers N. L., A short course on Banach space theory, London Math. Soc. Student Text., 64, Cambridge Univ. Press, Cambridge, 2005 | MR | Zbl

[12] Keller G., Moore L. C. (Jr.), “Invariant means on the group of integers”, Analysis and Geometry, Bibliographisches Inst., Mannheim, 1992, 1–18 | MR

[13] Cui Y., Hudzik H., Pluchenik R., “Extreme points and strongly extreme points in Orlicz spaces equipped with the Orlicz norm”, Z. Anal. Anwendungen, 22:4 (2003), 789–817 | DOI | MR | Zbl

[14] Lorentz G. G., “A contribution to the theory of divergent sequences”, Acta Math., 80 (1948), 167–190 | DOI | MR | Zbl

[15] Luxemburg W. A. J., “Nonstandard hulls, generalized limits and almost convergence”, Analysis and Geometry, Bibliographisches Inst., Mannheim, 1992, 19–45 | MR

[16] Nillsen R., “Nets of extreme Banach limits”, Proc. Amer. Math. Soc., 55:2 (1976), 347–352 | DOI | MR | Zbl

[17] Rickart Ch. E., General theory of Banach algebras, Univ. Ser. Higher Math., D. Van Nostrand Co., Princeton, N.J., 1974 | MR

[18] Sucheston L., “Banach limits”, Amer. Math. Monthly, 74:3 (1967), 308–311 | DOI | MR | Zbl

[19] Semenov E. M., Sukochev F. A., “Invariant Banach limits and applications”, J. Funct. Anal., 256:6 (2010), 1517–1541 | DOI | MR

[20] Semenov E. M., Sukochev F. A., “Extreme points of the set of Banach limits”, Positivity, 17:1 (2013), 163–170 | DOI | MR | Zbl

[21] Semenov E. M., Sukochev F. A., Usachev A. S., “Geometricheskie svoistva mnozhestva banakhovykh predelov”, Izv. RAN. Ser. mat., 78:3 (2014), 177–204 | DOI | MR | Zbl

[22] Talagrand M., “Geometrie des simplexes de moyennes invariantes”, J. Funct. Anal., 34:2 (1979), 304–337 | DOI | MR | Zbl

[23] Chou C., “On the size of the set of left invariant means on a semigroup”, Proc. Amer. Math. Soc., 23:1 (1969), 199–205 | MR | Zbl

[24] Eberlein W. F., “Banach–Hausdorf limits”, Proc. Amer. Math. Soc., 1:5 (1950), 662–665 | DOI | MR | Zbl