I have been doing some research on fixed point theorems, and they have brought me around to papers from the 1960s in functional analysis in Banach spaces.
I think that today it is common practice to use either $\langle\cdot,\cdot\rangle$ or $(\cdot,\cdot)$ to mean an inner product in a Hilbert space. However, in these papers, they use the latter notation to mean something different: here, the first argument is a bounded conjugate linear functional from $V$, the second argument is in $V$, and $(f,x)=f(x)$.
Is there some reason that these two seemingly disparate concepts have the same notation? I do not know a lot of the language in linear algebra so I am a bit out of my league in terms of looking things up.