I am reading the paper "REPRESENTATION AND INDEX THEORY FOR TOEPLITZ OPERATORS" by Gerald Murphy and came across this passage:
I was wondering why we care about the strict topology or why is it important for multiplier algebra. So I know how these are defined but I've never understood why we should use it. Am I supposed to assume we are talking about the strict topology every time I see the multiplier algebra?
Now for this specific example given below for the Toeplitz matrix, why is it better to identify the operators on Hardy space with the multiplier algebra when talking about convergence?