# On “An elementary proof of a fundamental theorem in the theory of Banach algebras” by C.E.Rickart

I am reading "An elementary proof of a fundamental theorem in the theory of Banach algebras" by C.E.Rickart, available for instance on https://projecteuclid.org/euclid.mmj/1028998012

The concepts of "circle operation", quasi-regularity and quasi-inverses are new to me, so I am trying to understand every individual formula in detail.

It is interesting how Rickart is using here formally an identity element, although this might be actually not existing. Now when I did the calculation following "An application of this relation, along ... gives" myself, I got $$(1-x^0)h(1-x^0)=hk-x^0hk-k$$

Please mark the term $$-x^0hk$$ in my right-hand side instead of $$+x^0hk$$ in the screenshot. Is this observation correct, i.e. is the "+" in the screenshot a typo?

The rest of the proof of continuity of quasi-inversion goes through without change and is clear to me.