Operator algebra is a branch of mathematics that studies operators, which are functions that act on elements of a space, often in the context of Hilbert spaces or Banach spaces. It focuses on the algebraic properties of these operators, such as addition, multiplication, and composition, and how they can be represented and manipulated. In operator algebra, concepts like bounded operators and unbounded operators are essential, as they help define the behavior of operators in various mathematical contexts. This field has applications in quantum mechanics, where operators represent physical observables, and in functional analysis, which explores the properties of functions and their transformations.