I'm relatively new to MO (but have been on MSE for a longer time), which means that I don't have enough reputation to create new tags. Which is probably a good thing.
Lately I've been puzzling with Banach space tensor products and the approximation property, and on multiple occasions found that my search would have been easier if there had been a tag for questions related to the approximation property. It is my impression that it is a whole field of its own, with a rich body of theory and (especially) counterexamples, so to me a tag
approximation-property would make sense.
Since I understand that we don't want to go haphazardly creating new tags for every specialization (or niche) within mathematics, I thought I'd ask what you think. Has this been considered before? Do we like the idea? Do we hate it? Should we consider variations on the proposal (e.g. a tag
Added later: as per François' suggestion, here is my suggested tag info.
For questions relating to various approximation properties in functional analysis and (abstract) harmonic analysis, including approximation properties of Banach spaces, locally convex spaces, operator algebras, and locally compact groups.
Furthermore, I tried to compile a list of questions to which the new tag would apply. Note that this list might be incomplete, again because I found it difficult to find all relevant questions on this topic. (Some would only mention the term "AP", so those would be hard to track down. This applies to one of the questions below – I only found it because it happened to be linked to another question on my list.)
Questions directly related to the approximation property (sorted by publication date).
Questions tangentially related to the approximation property (sorted by publication date).
Questions containing the term "approximation property" which nevertheless fall outside the scope of the proposed tag (mostly regarding different approximation properties, e.g. in algebra or logic).
- Real approximation for homogeneous spaces of linear algebraic groups
- Infinitely many solutions of a diophantine equation
- What could be some potentially useful mathematical databases?
- Class number of PGL_2
- Are there lightweight foundations for arbitrarily extendable objects?
- Analytic elements in non-archimedean geometry
- Is there a truth approximation on a cumulative hierarchy?
- A cohomology group which depends on the connection
- Preserving Jonsson cardinals
- The $\delta$-approximation property for ground models
- If the finitely additive measure of an open set is approximable by clopen sets, is it approximable from within?