We propose a formalization of the concept of ‘having the permission to say something to somebody’. For it, we introduce a notion of private announcement and define a permission operator with agency. We prove that this can be seen as a generalisation of the notion of permitted public announcement Balbiani and Seban (2011). We also add a notion of obligation with a new intuition. We illustrate th...

ACP is combined with Belnap’s four-valued logic via conditional composition (if–then–else). We show that the operators of ACP can be seen as instances of more general, conditional operators. For example, both the choice operator + and δ (deadlock) can be seen as instances of conditional composition, and the axiom x + δ = x follows from this perspective. Parallel composition is generalized to th...

Let X and Y be complex Banach spaces and BX resp. BY the closed unit ball. Analytic maps φ : BY → BX and ψ : BX → C induce the weighted composition operator: Cφ,ψ : H(BY) → H(BX), f 7→ ψ(f ◦ φ), whereH(BY) resp. H(BX) denotes the collection of all analytic functions f : BX(resp.BY) → C.We study when such operators acting between weighted spaces of analytic functions are isometric. RESUMEN Sea X...

This paper generalizes the mixed extension principle in L2(R) of [50] to a pair of dual Sobolev spaces H(R) and H−s(Rd). In terms of masks for φ, ψ, . . . , ψ ∈ H(R) and φ̃, ψ̃, . . . , ψ̃ ∈ H−s(Rd), simple sufficient conditions are given to ensure that (X(φ;ψ, . . . , ψ), X−s(φ̃; ψ̃, . . . , ψ̃)) forms a pair of dual wavelet frames in (Hs(Rd),H−s(Rd)), where X(φ;ψ, . . . , ψ) := {φ(· − k) : k ∈ Zd} ...

Let A and B be separable C∗-algebras, A unital and B stable. It is shown that there is a natural six-terms exact sequence which relates the group which arises by considering all semi-split extensions of A by B to the group which arises by restricting the attention to unital semi-split extensions of A by B. The six-terms exact sequence is an unpublished result of G. Skandalis. Let A,B be separab...

Occurrences of a factor w in an infinite uniformly recurrent sequence u can be encoded by over finite alphabet. This is usually denoted du(w) and called the derived to u. If prefix fixed point primitive substitution φ, then Durand's result from 1998, ψ as well. For non-prefix w, only exceptionally. To study this phenomenon we introduce new notion: A set M substitutions said closed under derivat...

Let Dn be the unit polydisc of Cn. The class of all holomorphic functions with domain Dn will be denoted by H(Dn). Let φ be a holomorphic self-map of Dn, the composition operator Cφ induced by φ is defined by (Cφ f )(z) = f (φ(z)) for z ∈Dn and f ∈H(Dn). If, in addition, ψ is a holomorphic function defined on Dn, the weighted composition operator ψCφ induced by ψ and φ is defined by ψCφ(z) = ψ(...