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We determine when contractive idempotents in the measure algebra of a locally compact group commute. We consider a dynamical version of the same result. We also look at some properties of groups of measures whose identity is a contractive idempotent. [ABSTRACT FROM AUTHOR]

We consider the Fourier-Stieltjes algebra B (G) of a locally compact group G. We show that operator amenability of B (G) implies that a certain semitopological compactification of G admits only finitely many idempotents. In the case that G is connected, we show that operator amenability of B (G) entails that G is compact. [ABSTRACT FROM AUTHOR]

We address two errors made in our paper [7]. The most significant error is in Theorem 1.1. We repair this error, and show that the main result, Theorem 2.5 of [7] , is true. The second error is in one of our examples, Remark 2.4 (iv), and we partially resolve it. [ABSTRACT FROM AUTHOR]

We withdraw a claim from the paper [1] by the three first named authors. [ABSTRACT FROM AUTHOR]

We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely S U (n) , the Heisenberg group H , the reduced Heisenberg group H r , the Euclidean motion group E (2) and its simply connected cover E ˜ (2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate that "polynomially growing" weights do not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. [ABSTRACT FROM AUTHOR]