caa a22 4500 386385858 CHVBK 20180307112058.0 cr unu---uuuuu 161130e198901 xx s 000 0 eng 10.1017/S0305004100001419 doi S0305004100001419 pii (NATIONALLICENCE)cambridge-10.1017/S0305004100001419 Lifting results for sequences in Banach spaces [Elektronische Daten] Several important classes of Banach spaces are characterized by means of convergence properties of sequences. For example, if X is a Banach space, then X belongs to the class Nl1 of spaces without copies of l1, the class R of reflexive spaces or the class F of finite-dimensional spaces if and only if each bounded sequence has respectively a weakly Cauchy (w-Cauchy), weakly convergent (w-convergent) or convergent subsequence. Similarly X is in the class WSC of weakly sequentially complete spaces, or the class SCH of spaces with the Schur property if and only if each w-Cauchy sequence is w-convergent, or convergent, respectively; note that X SCH if and only if each w-convergent sequence of X is convergent (see [12], p. 47). Copyright © Cambridge Philosophical Society 1989 Gonzalez M. University of Santander, Spain Onieva V. M. University of Zaragoza, Spain Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 117-121 0305-0041 105:1<117 1989 105 PSP https://doi.org/10.1017/S0305004100001419 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0305004100001419 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gonzalez M. University of Santander, Spain NATIONALLICENCE 700 1- Onieva V. M. University of Zaragoza, Spain NATIONALLICENCE 773 0- Mathematical Proceedings of the Cambridge Philosophical Society Cambridge University Press 105/1(1989-01), 117-121 0305-0041 105:1<117 1989 105 PSP CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge