(Upon replacing the Euclidean structure by a Banach space structure, of course.)

]]>I think in (13) should be

*[Corrected, thanks – T.]*

Oops, that was a typo; what I meant to say here was that the images of H and K under the quotient map become groups that commute with each other (but need not be abelian).

]]>In Exercise 1.(7)，you say that H/[H,K],K/[H,K] become abelian.But I’m a bit confused with these words.Since [H,K] may not be a subgroup of H,and at this time we can not do the quotient operation.And even if [H,K] is a subgroup of H,the quotient group may still not abelian,for example K is the trivial group {1} and H nonabelian. ]]>

I think there are some problems in (7) and (8) and (10). It seems the position of Z in the first term in (7) is not true. Also, I don’t get the second identification that [0,y] := [1,y+x mod 1], isn’t it [0,y]=[1,y]?

*[Corrected, thanks – T.]*

in equation (13) there are some misprints concerning LaTeX.

Is there the possibility that there is a miscalculation on the second term?

Yours sincerersly,

Jordi-Lluis Figueras Romero

]]>