English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We are interested here in isomorphic invariants of the various Banach spaces associated with the spaces L°°Gu) for finite measures ju. (Throughout, "/*" and v denote arbitrary finite measures on possibly different unspecified measureable spaces.) We classify the spaces L°°(M) themselves up to isomorphism (linear homeomorphism) in §3, where we also obtain information on the spaces A and A* for subspaces A of L(jx). In §2, we give a short proof of a result (Corollary 2.2) which simultaneously generalizes the result of Pelczyiiski that L(jx) is not isomorphic to a conjugate space if fi is nonpurely atomic [7], and the result of Gel'fand that L[0, l ] is not isomorphic to a subspace of a separable conjugate space (c.f. [8]). We also obtain there that an injective double conjugate space is either isomorphic to /°° or contains an isomorph of /°°(r) for some uncountable set T, if it is infinite dimensional. (Henceforth, all Banach spaces considered are taken to be infinite dimensional. Also, we recall that a Banach space is called injective if every isomorphic imbedding of it in an arbitrary Banach space Y is complemented in F.) We include brief proofs of some of the results. Full details of the work announced here and other related work will appear in [ l l ] .

Some linear topological properties of $L^\infty$ of a finite measure space