TY - JOUR
AU - Hassan, Abdelgabar Adam
PY - 2023/12/31
Y2 - 2024/06/16
TI - Localized Automorphisms and Endomorphisms
JF - Communications in Mathematics and Applications
JA - Comm. Math. Appl.
VL - 14
IS - 5
SE - Research Article
DO - 10.26713/cma.v14i5.1971
UR - http://www.rgnpublications.com/journals/index.php/cma/article/view/1971
SP - 1575 - 1584
AB - <p>We give a practical criterion of invertibility of endomorphisms of \(O_n\) corresponding to unitaries in the normalizer of the diagonal inside the uniformly hyperfinite subalgebra. We also analyze the action of such localized automorphisms on the spectrum of the diagonal thus obtaining criteria of outerness. Unital endomorphisms of the Cuntz algebra \(O_n\) which preserve the canonical uniformly hyperfinite-subalgebra \(F_n \subseteq O_n\) are investigated. We give examples of such endomorphisms \(\lambda =\lambda_u\) for which the associated unitary element \(u\) in \(O_n\).</p>
ER -