Operator topologies
In the mathematical field of functional analysis there are several standard topologies which are given to the algebra B(X) of bounded linear operators on a Banach space X. == Introduction == Let ( T n ) n ∈ N {\displaystyle (T_{n})_{n\in \mathbb {N} }} be a sequence of linear operators on the Banach space X {\displaystyle X} . Consider the statement that ( T n ) n ∈ N {\displaystyle (T_{n})_{n\in \mathbb {N} }} converges to some operator T {\displaystyle T} on X {\displaystyle X} .