Integral transforms of vector measures on semigroups with applications to spectral operators.
We study the subset in a unital C*-algebra composed of elements a such that is invertible, where denotes the Moore-Penrose inverse of a. A distinguished subset of this set is also investigated. Furthermore we study sequences of elements belonging to the aforementioned subsets.
A characterization of isometries of complex Musielak-Orlicz spaces is given. If is not a Hilbert space and is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all . Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.
We will discuss Kellogg's iterations in eigenvalue problems for normal operators. A certain generalisation of the convergence theorem is shown.