Concept

Calkin algebra

Summary
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. Properties
  • Since K(H) is a maximal norm-closed ideal in B(H), the Calkin algebra is simple. In fact, K(H) is the only closed ideal in B(H).
  • As a quotient of a C*-algebra by a two-sided ideal, the Calkin algebra is a C*-algebra itself and there is a short exact sequence ::0 \to K(H) \to B(H) \to B(H)/K(H) \to 0 :which induces a six-term cyclic exact sequence in K-theory. Those operators in B(H) which are mapped to an invertibl
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading