Name that Theorem!  James Currie  12/6/95 12:00 AM  Could someone please give references for the following result? What extensions etc. are known? Theorem: Let f(x) be a real valued function of one real variable such James Currie, Math 
Name that Theorem!  Gareth McCaughan  12/6/95 12:00 AM  In article <Pine.OSF.3.91.951206111141.1482A100000@io.UWinnipeg.ca>, James Currie <cur...@io.UWinnipeg.ca> wrote: >Theorem: Let f(x) be a real valued function of one real variable such Presumably "whenever" means "if and only if" here? If f(x) is always 0  
Name that Theorem!  Robert Israel  12/6/95 12:00 AM  In article <Pine.OSF.3.91.951206111141.1482A100000@io.UWinnipeg.ca>, James Currie <cur...@io.UWinnipeg.ca> writes: > Theorem: Let f(x) be a real valued function of one real variable such This was proved by G. Waldenberg, American Mathematical Monthly 95 (1988) Let f: X > Y be a mapping of normed spaces such that \sum_{n=1}^\infty f(a_n) converges whenever \sum_{n=1}^\infty a_n converges (both in the norm topology). I have a slight additional extension (unpublished): Let f: X > Y be a mapping of Banach spaces such that \sum_{n=1}^\infty f(a_n) converges weakly whenever \sum_{n=1}^\infty a_n converges (strongly). Then  
Name that Theorem!  Gareth McCaughan  12/7/95 12:00 AM  In article <4a4nb3$3...@lyra.csx.cam.ac.uk>, I wrote: > In article <Pine.OSF.3.91.951206111141.1482A100000@io.UWinnipeg.ca>,
> Presumably "whenever" means "if and only if" here? If f(x) is always 0 A couple of people mailed me to point out that this is just fine, with c=0. However, I must apologise very completely, because even this is not So, I grovel. One of these years I'll manage to post something to
