Talk:Neumann Series Theorem

This is definitely a duplicate. Can't track down the page right now though. Caliburn (talk) 12:19, 23 June 2023 (UTC)

Probably you have this one in mind:

Invertibility of Identity Minus Operator

I know that a chunk of my work on continuous linear transformations already exists under the name of bounded linear transformations. However, compared to my source, the notational differences at times are a bit involved, and I did not want to start changing the notation in the middle of my book. But eventually this unfortunate problem has to be resolved. Is this how Mochizuki feels when he develops a completely different vocabulary for standard notions?--Julius (talk) 13:55, 23 June 2023 (UTC)

Also this Element of Unital Banach Algebra Close to Identity is Invertible --Usagiop (talk) 17:20, 23 June 2023 (UTC)

If this is a duplicate and/or an instance/generalisation one of the other, then we want to keep this name because it's a named theorem.

All merging of multiple instances of the same content is good. --prime mover (talk) 21:52, 23 June 2023 (UTC)

Also, bounded linear transformations have been developed beyond NVS, while I am confined to them, so merging has to be done very selectively.--Julius (talk) 22:18, 23 June 2023 (UTC)

I am still unsure why we would want to have different result pages for continuous linear transformations and bounded linear transformations, these are readily treated as synonyms in the context of NVSs. If you can extend results like these to say, continuous linear transformations between general TVSs or LCSs (or something more exotic inbetween) then this would be valuable. I haven't done much (any?) work on bounded linear transformations between TVSs that are not continuous. It is true in general that continuous linear transformations are bounded, and an easy sufficient condition for the converse being true is having the domain TVS be metrizable. (so for example, they are equivalent notions on Frechet spaces) Caliburn (talk) 13:54, 6 July 2023 (UTC)

I kept my own version of proof mostly because I wanted to avoid jumping to a different notation in the middle of my book. Eventually all matching pages should be merged, but then all the definition pages should inform about the differences in notation throughout the literature.--Julius (talk) 23:32, 6 July 2023 (UTC)

All results referred to here are about Banach space. Nothing about TVS, LCS or NVS. --Usagiop (talk) 19:01, 6 July 2023 (UTC)

Please be more specific. In my sources, Banach spaces are special types of NVS, so one way or another, I have to refer to vector spaces and norms.--Julius (talk) 23:20, 6 July 2023 (UTC)