This analysis reveals the connection between the simplicity of lp-operator graph algebras and Leavitt path algebras, highlighting implications for algebraic structures.
For each finite p⩾1 and each countable directed graph E we consider the Leavitt path C-algebra L(E) and the Lp-operator graph algebra Op(E). We show that the (purely infinite) simplicity of Op(E) as a Banach algebra is equivalent to the (purely infinite) simplicity of L(E) as a ring.
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Cortiñas⋆ et al. (2025) studied this question.
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