Calkin algebra
= Calkin algebra
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{title2=$\mathcal Q(H)=B(H)/\mathcal K(H)$}
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For an infinite-dimensional complex <Hilbert space>, the Calkin algebra is the unital quotient of the <bounded operators> by the closed two-sided ideal of <compact operators>. Its spectrum records invertibility up to compact errors. An operator is <Fredholm> exactly when its image in this quotient is invertible.