Talk:Riesz space

Lattice vectors?

Are lattice vectors the same as vector lattices? I don't think they are. Lattice vectors are used to indicate the crystal structure in crystalline solids, and they're formatted as (0,a,0). Maybe clarify within the article whether they are or are not the same.Jojojlj (talk) 23:33, 1 June 2012 (UTC)

These two concepts have little do to with each other. I added a hatnote. - Saibod (talk) 08:21, 21 June 2012 (UTC)

Feel free to improve on the hatnote. - Saibod (talk) 08:22, 21 June 2012 (UTC)

Definition

I think the definition needs more detail. What does it mean that the lattice structure is "compatible" with the vector space structure? - Saibod (talk) 08:21, 21 June 2012 (UTC)

Agreed, I made some improvements MikeRumex (talk) 22:06, 9 August 2012 (UTC)

Wrong definition of Archimedean, I think. There are two closely related. Should be as in Infinite Dimensional Analysis: A hitch-hikers guide, defn 8.2 I think. There's also an explanation there: needs checking.

Spelling

"Principle projection property" seems wrong to me. Shouldn't it be "principal projection property"? Infenwe (talk) 01:50, 27 October 2012 (UTC)

Complex Riesz spaces

I think the article should also give a treatment of complex Riesz spaces (where the field is C instead of R). See e.g.:

• Riesz Spaces II by Adriaan Zaanen (1983)
• Introduction to Operator Theory in Riesz Spaces by Adriaan Zaanen (1997)
• Banach Lattices by Peter Meyer-Nieberg (1991)
• Banach Lattices and Positive Operators by Helmut Schaefer (1975)
• Banach Spaces of Continuous Functions as Dual Spaces by Dales et al. (2016)

Thatsme314 (talk) 19:02, 19 January 2022 (UTC)