Harmonic calculus in involutive \(p\)-Banach algebras and applications
Let \(A\) be a complex \(p\)-Banach algebra with \(0<p\leq 1\) which is endowed with a conjugate-linear involution \(*\). If \(a\in A\), then the authors define \(f(a)\) for any harmonic function \(f\) on a simply connected domain containing the spectrum of \(a\) by \(f(a)= g(a)+ h(a)^*\), where \(g\) and \(h\) are holomorphic functions such that \(f= g+ \overline h\). A number of features (including uniqueness, continuity, and a spectral mapping theorem) and applications (such as a square root lemma and analogues of the K. Fan and J. von Neumann inequalities) are shown.
scientific article; zbMATH DE number 1931531