Some Observations About "Moving Norms'' in Normed Algebras

In this note one tries to venture into a study of some notions, in the context of a (unital) normed algebra, in particular the algebra of operators on a Hilbert space. Namely, one considers ``moving norms’', i.e.\ norming an element minus a scalar multiple of the unity and related notions, and goes into obtaining some rather nice assertions.