A Wide Class of Ultrabornological Spaces of Measurable Functions

✍ Scribed by S. Diaz; A. Fernandez; M. Florencio; P.J. Paul

• Book ID: 102972759
• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 723 KB
• Volume: 190
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1995.1104

✦ Synopsis

Our main result states that a bornological locally convex space having a suitable Boolean algebra of projections is ultrabornological. This general theorem, whose proof is a variation of the sliding-hump techniques used in [Díaz et al., Arch. Math. (Basel) 60 (1993), 73-78; Díaz et al., Resultate Math. 23 (1993), 242-250; Drewnowski et al., Proc. Amer. Math. Soc. 114 (1992), 687-694; Drewnowski et al., Atti Sem. Mat. Fis. Univ. Modena 41 (1993), 317-329], is applied to prove that some non-complete normed spaces such as the spaces of Dunford, Pettis, or McShane integrable functions, as well as other interesting spaces of weakly or strongly measurable functions, are ultrabornological. We also give applications to vector-valued sequence spaces; in particular, we prove that (\ell^{p}{X}(1 \leq p<\infty)) is an ultrabornological DF-space when (X) is. 1994 Academic Press, Inc.