Wong, Pak-Ken The second conjugate algebras of Banach algebras. (English) Zbl 0818.46055 Int. J. Math. Math. Sci. 17, No. 1, 15-18 (1994). Arens regularity for a Banach algebra \(A\) is defined by the identity of the two natural Arens multiplications on \(A^{**}\). The author shows, among other characterizations of Arens regularity, that, if each continuous linear map of \(A\) into \(A^*\) is weakly compact, then \(A\) is Arens regular. From this it is deduced that a \(B^*\)-algebra is Arens regular. It is also shown that a closed subalgebra inherits Arens regularity. Reviewer: S.Swaminathan (Halifax) MSC: 46H10 Ideals and subalgebras 46H05 General theory of topological algebras 46H99 Topological algebras, normed rings and algebras, Banach algebras Keywords:Arens regularity; Arens multiplications; \(B^*\)-algebra is Arens regular; closed subalgebra inherits Arens regularity PDFBibTeX XMLCite \textit{P.-K. Wong}, Int. J. Math. Math. Sci. 17, No. 1, 15--18 (1994; Zbl 0818.46055) Full Text: DOI EuDML