Calkin correspondence

Calkin correspondence refers to a specific relationship in the field of functional analysis, particularly concerning the study of bounded linear operators on a Hilbert space. It is named after mathematician Julius Calkin. In essence, Calkin correspondence involves the establishment of a certain equivalence relation on bounded operators and the subsequent construction of a quotient space. The key points are as follows: 1. **Bounded Linear Operators**: Consider a Hilbert space \(H\).