From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) Subject: Re: Compact of L_infinity Date: 5 Oct 1999 13:27:05 -0400 Newsgroups: sci.math In article <37FA0FCB.7E1EA624@inpg.fr>, Nicolas Marchand wrote: :Hi, : :What are the compact subsets of L_infinity ? Theoretically, L_infinity is isomorphic (as a Banach lattice) to C(Y) for a compact Hausdorff Y. So, a form of Arzela-Ascoli theorem can be put together, but the formulation would be "excessively cumbersome", as Dunford-Schwartz note in a similar situation (IV.15). This Y will be extremely disconnected, and non-metrizable in the interesting situations. >Can i extract a convergent series from a series (f_n) of essentially >bounded functions (same bound) ? Not always (and you probably mean "sequences"): in L_infinity(0,1), take any list of characteristic functions of open intervals with rational endpoints; the distance between any two members is exactly 1. Cheers, ZVK(Slavek). ============================================================================== From: "G. A. Edgar" Subject: Re: Compact of L_infinity Date: Tue, 05 Oct 1999 14:07:22 -0400 Newsgroups: sci.math In article <7tdcd9$i3b@mcmail.cis.McMaster.CA>, Zdislav V. Kovarik wrote: > This Y will be extremely disconnected also extremally disconnected -- Gerald A. Edgar edgar@math.ohio-state.edu Department of Mathematics telephone: 614-292-0395 (Office) The Ohio State University 614-292-4975 (Math. Dept.) Columbus, OH 43210 614-292-1479 (Dept. Fax)