Principal subalgebra

In the context of algebra and functional analysis, a **principal subalgebra** typically refers to a specific type of subalgebra that is generated by a single element, particularly in the study of operator algebras, such as von Neumann algebras or C*-algebras. To elaborate, let's consider the following definitions: 1. **Subalgebra**: A subalgebra of an algebra is a subset of that algebra that is itself an algebra under the same operations.