For example in Atiyah's $KR$-theory there is the notion of a *Real vector bundle* in contrast to complex or real vector bundles. I am also familiar with the notion of a Real $C^\*$-algebra and there are probably a lot more objects with sensible definitions of *Real*.


However Atiyah did not use a capitalized *Real* in his paper "K-theory and reality", so my question is: 



> 
> Whose ideas was it to write *Real* instead of *real*?
> 
> 
> 


I would also be interested in the general history of this notion, but that's probably too much to ask for (judging from remarks in the above mentioned paper I suspect it starts somewhere in algebraic geometry – of which I hardly know anything.)



Who was the first to capitalize Real?
Apparently, Atiyah himself thinks he invented the notation:


![](https://ilorentz.org/beenakker/MO/Real.png)


(quote from his [collected works](https://books.google.nl/books?id=XHnWhjQZpkUC&pg=PA620&lpg=PA620&dq=Real+vector+bundle+with+capital+R&source=bl&ots=Ay51I5tFlY&sig=5Qilhujr56C8TtXuMNC0nchzrS8&hl=en&sa=X&ved=0ahUKEwiW8_mH1L7aAhUPzqQKHQZKBMIQ6AEIUDAD#v=onepage&q&f=false))


