Mehta, H. S.; Mehta, R. D.; Patel, D. R. Peripheral spectrum for \(A \times B\). (English) Zbl 1355.46046 Sci. Math. Jpn. 78, No. 2, 135-138 (2015). Let \(A\) be a function algebra on a compact Hausdorff space \(X\). The authors study the maximum modulus set of an element \(h=(f,g)\in A\times B\) and its peripheral spectrum \[ \sigma_\pi(h)=\sigma(h)\cap \{z\in \mathbb C:\| h\|=|z|\} \] within the Cartesian product \(A\times B\) of two function algebras and where \(\| h\|=\max\{\| f\|_\infty, \| g\|_\infty\}\). Some observations on the set of peaking functions for \(A\times B\) are given, too. Reviewer: Raymond Mortini (Metz) MSC: 46J10 Banach algebras of continuous functions, function algebras Keywords:function algebras; peripheral spectrum; maximum modulus sets; Cartesian product; peak function PDFBibTeX XMLCite \textit{H. S. Mehta} et al., Sci. Math. Jpn. 78, No. 2, 135--138 (2015; Zbl 1355.46046) Full Text: Link Link