What Does T|A with a Half Upward Arrow Mean in Notation for Linear Operators?

[jostpuur]

I encountered notation that I don't know. It's like T|A where T is a mapping, and A is a set (little like a restriction), but the | is an arrow pointing upwards and the left hook is missing like with an arrow of a weak convergence.

Anyone knowing what that means? Or a keyword that I could put in google (I cannot put that half arrow there)

 

[Hurkyl]

What is the context?

 

[jostpuur]

Operators. T:X->X is a continuous linear mapping in a Banach space, and an ascent of the operator is defined

$$\textrm{ascent}(T) := \textrm{min}\;\{p\in\mathbb{N}\;|\; \textrm{ker}(T^p)=\textrm{ker}(T^{p+1})\}$$

The p is then assumed to be the ascent, and the notation

$$T\upharpoonright T^p(X)$$

is used. This notation means some kind of mapping, because it is said to be invertible.