I have heard of constructing a Banach algebra of functions by defining the multiplicative operation as function composition. What is the formal name for this sort of construction? What work has been done on questions such as: if $\mathcal{B}$ is a compositional Banach algebra of functions and $f,g\in \mathcal{B}$, then do we have $\|g\circ f\| \leq \|g\|\|f\|$? When does equality hold? Apologies for the basic question.
2026-02-22 19:30:34.1771788634
Banach algebra of functions under composition
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