Calkin algebra

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.