Robin Harte Dedicated to Goldie Hawn, on her birthday Abstract We attempt to deconstruct the Arens-Royden Theorem. Suppose A is a Banach algebra (by default complex, with identity 1): we shall write 0.1 A−1 = {a ∈ A : 1 ∈ Aa∩aA} for the open subgroup of invertible elements, and A−1 0 for the connected component of the identity in A −1: it turns out ([8], [11] Theorem 7.11.4) that 0.2 A−1 0 = Ex...

To every compact orientable surface one can associate following Harvey Ha Ha a combinatorial object the so called complex of curves which is analogous to Tits buildings associated to semisimple Lie groups The basic result of the present paper is an analogue of a fundamental theorem of Tits for these complexes It asserts that every automorphism of the complex of curves of a surface is induced by...

Let G be a locally compact non-compact group. We show that under a very mild assumption on the weight function w, the weighted group algebra L1(G, w) is strongly Arens irregular in the sense of [Dal–Lam–Lau 01]. To this end, we first derive a general factorization theorem for bounded families in the L∞ ( G, w ) ∗ -module L∞ ( G, w ) .

The notion of ultrametrics can be considered as a zero-dimensional analogue ordinary metrics, and it is expected to prove ultrametric versions theorems on metric spaces. In this paper, we provide the Arens-Eells isometric embedding theorem spaces, Hausdorff extension Niemytzki-Tychonoff characterization compactness, author’s interpolation metrics dense subsets spaces metrics.

Let $fM(X)$ be the  space of  all finite regular Borel measures on $X$. A general measure algebra is a subspace  of$fM(X)$,which is an $L$-space and has a multiplication preserving the probability measures. Let $cLsubseteqfM(X)$ be a general measure algebra on a locallycompact space $X$. In this paper, we investigate the relation between Arensregularity of $cL$ and the topology of $X$. We  find...

We give a characterization of all cartesian products D1 × D2 ⊂ C for which the Kobayashi–Royden and Hahn pseudometrics coincide. In particular, we show that there exist domains in C for which Kobayashi–Royden and Hahn pseudometrics are different.