Calkin algebra

In functional analysis, the Calkin algebra, named after John Williams Calkin,^[1] 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.^[2] 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.

^ "A Community of Scholars, the Institute for Advanced Study, Faculty and Members 1930–1980" (PDF). ias.edu. Archived from the original (PDF) on 2011-11-24. Retrieved 2020-01-17.
^ Calkin, J. W. (1 October 1941). "Two-Sided Ideals and Congruences in the Ring of Bounded Operators in Hilbert Space". The Annals of Mathematics. 42 (4): 839. doi:10.2307/1968771.

[1] "A Community of Scholars, the Institute for Advanced Study, Faculty and Members 1930–1980" (PDF). ias.edu. Archived from the original (PDF) on 2011-11-24. Retrieved 2020-01-17.

[2] Calkin, J. W. (1 October 1941). "Two-Sided Ideals and Congruences in the Ring of Bounded Operators in Hilbert Space". The Annals of Mathematics. 42 (4): 839. doi:10.2307/1968771.

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