Operator algebra refers to https://en.wikipedia.org/wiki/Operator_(mathematics) https://en.wikipedia.org/wiki/Operator_(mathematics). An operator can be someth

Operator algebra refers to https://en.wikipedia.org/wiki/Operator_(mathematics) https://en.wikipedia.org/wiki/Operator_(mathematics). An operator can be something like the differentation operator (d/dx), the integral operator, gradient, curl, or other structure. Operators are similar to functions but work more generally, like mapping functions to other functions. See https://en.wikipedia.org/wiki/Quantum_field_theory#Canonical_quantization https://en.wikipedia.org/wiki/Quantum_field_theory#Canonical... for some of the applications/definitions in quantum mechanics. IIUC, Operator algebra is the study of the properties of operators just like real, complex, matrix, and linear algebra are the study of the properties of those objects/constructs. As such, once you have defined an operator for e.g. Schroedinger's wave equation you can manipulate and explore that using the rules and principles of operator algebra. Thus, making them easier to work with.