Norming Subspaces Isomorphic to l(1)

作者：Ostrovska Sofiya^*

来源：Acta Mathematica Sinica-English Series, 2015, 31(5): 767-771.

DOI：10.1007/s10114-015-4123-x

• Banach space
• norming subspace
• dual space
• weak* convergence
• free ultrafilter

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.

• 出版日期2015-5