Dilation (operator theory)

In operator theory, dilation refers to a specific concept particularly relevant in the study of linear operators on Hilbert spaces. The idea of dilation relates to the representation of certain types of operators (often bounded operators) in terms of larger, often simpler, operators. Dilation can be viewed from different perspectives, including matrix dilation, functional analytic dilation, and quantum mechanical contexts. ### 1. **Unitary Dilation**: A common type of dilation in operator theory is unitary dilation.