where A,B ⊂ B(H), and the distance between A⊗Mn and B ⊗Mn is measured in B(H) ⊗ Mn ∼= B(H). We also investigate the consequences of “complete closeness”, i.e. what can be said when dcb(A,B) is small? For example, if dcb(A,B) is small, then any projection p ∈ A ⊗ Mn can be suitably approximated by a projection q ∈ B ⊗ Mn, leading an isomorphism K0(A) → K0(B) which maps [p]0 to [q]0. This strateg...

It is proved that the unital Banach algebra of almost periodic functions of several variables with Bohr-Fourier spectrum in a given additive semigroup is an Hermite ring. The same property holds for the Wiener algebra of functions that in addition have absolutely convergent Bohr-Fourier series. As applications of the Hermite property of these algebras, we study factorizations of Wiener–Hopf typ...

In this paper we investigate Hartman functions on a topological group G. Recall that (ι, C) is a group compactification of G if C is a compact group, ι : G → C is a continuous group homomorphism and ι(G) ⊆ C is dense. A bounded function f : G 7→ C is a Hartman function if there exists a group compactification (ι, C) and F : C → C such that f = F ◦ ι and F is Riemann integrable, i.e. the set of ...

Let K be a field of characteristic not two or three with an involution and F be its fixed field. Let Hm be the F -vector space of all m-square Hermitian matrices over K. Let ρm denote the set of all rank-one matrices in Hm. In the tensor product space ⊗ k i=1 Hmi , let ⊗ k i=1 ρmi denote the set of all decomposable elements ⊗ k i=1 Ai such that Ai ∈ ρmi , i = 1, . . . , k. In this paper, additi...