Embedding C*-algebras into the Calkin algebra of ℓp

Let p is an element of (1, infinity). We show that there is an isomorphism from any separable unital subalgebra of B(& ell;(p))/K(& ell;(p)) onto a subalgebra of B(& ell;(p))/K(& ell;(p)) that preserves the Fredholm index. As a consequence, every separable C*-algebra is isomorphic to a subalgebra of B(& ell;(p))/K(& ell;(p)). Another consequence is the existence of operators on B p that behave like the essentially normal operators with arbitrary Fredholm indices in the Brown-Douglas-Fillmore theory. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.