Completions with respect to total nonnorming subspaces

M. I. Ostrovskii

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., 31064, Kharkov, Ukraine

Abstract: The structure of completions of Banach spaces with respect to total nonnorming subspaces of dual spaces is studied. The obtained results imply, in particular, that such completions can be non-isomorphic to quotients of the space. In a separable case any one of the completions is isomorphic to a completion of $l_1$.

Received: 01.09.1997

Language: English

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