Talk:Minkowski Functional of Convex Absorbing Set is Finite

It's an interesting notational point, but I have seen "take $t > 0$" (where $t$ has been taken in $\C$) before. Of course since it's supposed to read the same as "take $t \in \R$ and $t > 0$", we should just write $t \in \R_{> 0}$, as I will do. Caliburn (talk) 07:27, 15 June 2023 (UTC)

Can it also be confirmed what $t A$ means? One expects it's "scalar product" as defined on a vector space, which in this context means "the restriction of the scalar product to $\R \times X$, and one intuitively wants to interpret it as Definition:Subset Product -- but this really needs to be made clear. --prime mover (talk) 07:58, 15 June 2023 (UTC)

This is the dilation of $A$ by $t$. That is, $t A = \set {t a : a \in A}$. I have put up a definition page for this so I had no excuse for not linking it. Caliburn (talk) 08:05, 15 June 2023 (UTC)

Ah right okay, so it does mean what we expect it to mean, which is good.

I will leave you to add that link to all those pages that need it.

I'm still trying to get my head round the arbitrary nature of the fact that this-all seems to be defined for the special case of a vector space over the complex plane where the domain is another seemingly special case of "the subset of this in which this mapping makes sense". Can this concept be applied to a general Banach space, for example? If so, what would $t$ be in such a context?

You're dead right, I don't have the slightest clue what I'm talking about. --prime mover (talk) 08:16, 15 June 2023 (UTC)