Open AccessSome dual Tauberian embeddings
Author(s) -
Olav Nygaard
Publication year - 2001
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2001.05.03
Subject(s) - embedding , dual (grammatical number) , star (game theory) , mathematics , banach space , operator (biology) , set (abstract data type) , space (punctuation) , discrete mathematics , abelian and tauberian theorems , pure mathematics , dual space , mathematical analysis , computer science , artificial intelligence , art , biochemistry , chemistry , literature , repressor , transcription factor , gene , programming language , operating system
We show that if the famous construction of Davis, Figiel, Johnson and Pełczyński [1] is worked out on a weak-star compact set in a dual Banach space, then the resulting Banach space is a dual space. Next we apply this result to show that either a set is weak-star thick or it is contained in the operator range of a weak-star continuous Tauberian embedding. This result improves and, in some sense, completes the theory of thin sets and surjectivity described in [8].