We give a simple proof of the maximality of dual coactions on full cross-sectional C*-algebras of Fell bundles over locally compact groups. This result was only known for discrete groups or for saturated (separable) Fell bundles over locally compact groups. Our proof, which is derived as an application of the theory of universal generalised fixed-point algebras for weakly proper actions, is different from these previously known cases and works for general Fell bundles over locally compact groups....

Given a unital C*-algebra $$𝒜$$ and a right C*-module $$𝒳$$ over $$𝒜$$ , we consider the problem of finding short smooth curves in the sphere $${𝒮}_{𝒳}$$ = x ∈ $$𝒳$$ : 〈x, x〉 = 1. Curves in $${𝒮}_{𝒳}$$ are measured considering the Finsler metric which consists of the norm of $$𝒳$$ at each tangent space of $${𝒮}_{𝒳}$$ . The initial value problem is solved, for the case when $$𝒜$$ is a von Neumann algebra and $$𝒳$$ is selfdual: for any element x 0 ∈ $${𝒮}_{𝒳}$$ and any tangent vector ν at x 0, there exists a curve γ(t) = e tZ(x 0), Z ∈ $${ℒ}_{𝒜}\left(𝒳\right)$$ , Z* = −Z and ∥Z∥ ≤ π, such...

Let t be a regular operator between Hilbert C*-modules and $t^{†}$ be its Moore-Penrose inverse. We investigate the Moore-Penrose invertibility of the Gram operator t*t. More precisely, we study some conditions ensuring that $t^{†}={(t*t)}^{†}t*=t*{(tt*)}^{†}$ and ${(t*t)}^{†}=t^{†}t{*}^{†}$. As an application, we get some results for densely defined closed operators on Hilbert C*-modules over C*-algebras of compact operators.

The paper the title refers to is that in Proceedings of the Edinburgh Mathematical Society, 40 (1997), 367-374. Taking it as an excuse we intend to realize a twofold purpose: 1° to atomize that important result showing by the way connections which are out of favour, 2° to rectify a tiny piece of history. The objective 1° is going to be achieved by adopting means adequate to goals; it is of great gravity and this is just Mathematics. The other, 2°, comes...