In functional analysis, the Calkin algebra, named after John Williams Calkin, is the quotient of B(H), the ring of bounded linear operators on a separable infinite-dimensional Hilbert space H, by the ideal K(H) of compact operators. Here the addition in B(H) is addition of operators and the multiplication in B(H) is composition of operators; it is easy to verify that these operations make B(H) into a ring. When scalar multiplication is also included, B(H) becomes in fact an algebra over the same field over which H is a Hilbert space.