In the Cohen model of set theory, the C*-algebra (c0(2^ω))^N does not embed into the Calkin algebra Q(ℓ2), although c0(2^ω) itself always does.
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Products of C*-algebras that do not embed into the Calkin algebra
In the Cohen model of set theory, the C*-algebra (c0(2^ω))^N does not embed into the Calkin algebra Q(ℓ2), although c0(2^ω) itself always does.