Ultrapowers and Local Properties of Banach Spaces

Jacques Stern
1978 Transactions of the American Mathematical Society  
The present paper is an approach to the local theory of Banach spaces via the ultrapower construction. It includes a detailed study of ultrapowers and their dual spaces as well as a definition of a new notion, the notion of a «-extension of a Banach space. All these tools are used to give a unified definition of many classes of Banach spaces characterized by local properties (such as the tp -spaces). Many examples are given; also, as an application, it is proved that any tp -space, 1 < p < oo,
more » ... space, 1 < p < oo, has an ultrapower which is isomorphic to an L^-space. [15].
doi:10.2307/1998816 fatcat:xeorwgepbjhqfeizkjiigze6pe