Journal of Operator Theory

Volume 94, Issue 1, Summer 2025 pp. 93-109.

Simplicity of $L^p$-graph algebras

Authors: Guillermo Cortinas (1), Diego Montero (2), Maria Eugenia Rodriguez (3)
Author institution:(1) Departamento Matematica-IMaS, FCEyN-UBA, Ciudad Universitaria Pab I, 1428, Buenos Aires, Argentina
(2) Ciudad de Buenos Aires, Argentina
(3) Ciclo Basico Comun, UBA, Ciudad Universitaria 1428, Buenos Aires, Argentina

Summary: For each finite $p\geqslant 1$ and each countable directed graph $E$ we consider the Leavitt path $\mathbb{C}$-algebra $L(E)$ and the $L^p$-operator graph algebra $\mathcal O^p(E)$. We show that the (purely infinite) simplicity of $\mathcal O^p(E)$ as a Banach algebra is equivalent to the (purely infinite) simplicity of $L(E)$ as a ring.

DOI: http://dx.doi.org/10.7900/jot.2023aug30.2459
Keywords: $L^p$-graph algebra, Leavitt path algebra, Banach algebra simplicity, algebraic simplicity

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