×

Banach limits: invariance and functional characteristics. (English. Russian original) Zbl 1384.46017

Dokl. Math. 96, No. 1, 305-307 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 475, No. 1, 7-9 (2016).
Summary: Banach limits invariant with respect to the Cesàro transform are studied. New functional characteristics of Banach limits are introduced and studied.

MSC:

46B99 Normed linear spaces and Banach spaces; Banach lattices
46A35 Summability and bases in topological vector spaces
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] S. Banach, Theory of Linear Operations (Elsevier, Amsterdam, 1987; Regulyarnaya i Khaoticheskaya Dinamika, Izhevsk, 2001). · Zbl 0613.46001
[2] Lorentz, G. G., No article title, Acta Math., 80, 167-190 (1948) · Zbl 0031.29501 · doi:10.1007/BF02393648
[3] Sucheston, L., No article title, Am. Math. Monthly, 74, 308-311 (1967) · Zbl 0148.12202 · doi:10.2307/2316038
[4] Eberlein, W. F., No article title, Am. Math. Soc. Proc., 1, 662-665 (1950) · Zbl 0039.12102 · doi:10.1090/S0002-9939-1950-0038009-0
[5] Dodds, P. G.; Pagter, B.; Sedaev, A. A.; Semenov, E. M.; Sukochev, F. A., No article title, Izv.: Math., 67, 1187-1212 (2003) · Zbl 1075.46028 · doi:10.1070/IM2003v067n06ABEH000461
[6] Semenov, E. M.; Sukochev, F. A., No article title, J. Funct. Anal., 256, 1517-1541 (2010) · Zbl 1205.46012 · doi:10.1016/j.jfa.2010.05.011
[7] Alekhno, E. A.; Semenov, E. M.; Sukochev, F. A.; Usachev, A. S., No article title, St. Petersburg Math., 28, 299-321 (2017) · Zbl 1373.46008 · doi:10.1090/spmj/1452
[8] Alekhno, E. A.; Semenov, E. M.; Sukochev, F. A.; Usachev, A. S., No article title, C. R. Acad. Sci. Paris Ser., 1, 1195-1199 (2016) · Zbl 1358.46018 · doi:10.1016/j.crma.2016.10.007
[9] Chow, C., No article title, Proc. Am. Math. Soc., 23, 199-205 (1969) · Zbl 0188.19006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.