For some reason, I have to work with Trotter product formula recently, but I do not have a strong background in functional analysis.
The following is the statement of the formula from MathWorld
When A and B are self-adjoint operators, $$ e^{t(A+B)} = \lim_{n \to +\infty}(e^{tA/n}e^{tB/n})^n $$
My questions are:
What does the exponential of an operator mean precisely?
How to interpret the convergence? In terms of some norm?