caa a22 4500 605462011 CHVBK 20210128100246.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10114-015-4123-x doi (NATIONALLICENCE)springer-10.1007/s10114-015-4123-x Ostrovska Sofiya Department of Mathematics, Atilim University, 06836, Incek, Ankara, Turkey aut Norming subspaces isomorphic to ℓ 1 [Elektronische Daten] [Sofiya Ostrovska] Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to ℓ 1 provided that the following two conditions are satisfied: (1) X* contains a subspace isomorphic to ℓ 1; and (2) X* contains a separable norming subspace. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 Banach space nationallicence norming subspace nationallicence dual space nationallicence weak* convergence nationallicence free ultrafilter nationallicence Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/5(2015-05-01), 767-771 1439-8516 31:5<767 2015 31 10114 https://doi.org/10.1007/s10114-015-4123-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10114-015-4123-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ostrovska Sofiya Department of Mathematics, Atilim University, 06836, Incek, Ankara, Turkey aut NATIONALLICENCE 773 0- Acta Mathematica Sinica, English Series Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 31/5(2015-05-01), 767-771 1439-8516 31:5<767 2015 31 10114