Erratum to “Arens regularity of the algebra 𝐴⊗𝐵”
A. Ülger · Transactions of the American Mathematical Society · 2003
have informed me that Theorem 4.20 in the last section of [1], which states that the projective tensor product C(K) C(S) of two commutative C * -algebras is Arens regular, is not correct. The reason, as they have rightly told me, is that, if G is a compact group, then the algebra C(G) C(G) contains an isomorphic copy of the Fourier algebra A(G), which is known to be not Arens regular. Consequently, C(G) C(G) is not Arens regular either. Unfortunately, this mistake also affects the subsequent results (from 4.21 to 4.27