# operator theory background

Mathematics is often divided into Analysis and Algebra. I want to know under which area Operator Theory lies. I have studied functional analysis where we studied operators on infinite dimensional spaces. I have come across terms like operator algebra and got confused whether it is a part of algebra or analysis. I want to study operator theory so I would like to know which is required more - Algebra or Analysis?

Functional analysis, as you may know, is the study of vector spaces endowed with a topology, the so-called topological vector spaces (TVS), and operators on topological vector spaces that respect these two combined structures: namely, linear operators that are continuous with respect to the underlying topologies. In operator theory, one focuses on these operators, their properties, and collections of operators with possibly additional algebraic structure, such as $C^*$-algebras and von Neumann algebras.