C*-algebras | K-theory | Operator theory

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. (Wikipedia).

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Related pages

Compact operator on Hilbert space | John Williams Calkin | Linear map | Hilbert space | Banach space | Functional analysis | Quotient space (linear algebra) | Ideal (ring theory) | Separable space | Fredholm operator | C*-algebra | Operator K-theory