Multiplicative maps into the spectrum

A weaker Gleason–Kahane–Żelazko theorem for modules and applications to Hardy spaces

“…And as in the proof of Proposition 2.2 we can show that χ(a)1 − a / ∈ A −1 for every a ∈ A. Now the result is a consequence of [11,Theorem 2.1], which states the following:…”

“…Under what condition can a multiplicative-like map on a Banach module be linear? It turns out that this depends on the analyticity of an associated map, as in [11].…”

“…At the end we give some applications to linear functionals on Hardy spaces. Of late, some problems along similar lines have been studied, for example in [11], where in the case of a Banach algebra A it is investigated when a continuous multiplicative map φ : A → C with values φ(x) in the spectrum of x is automatically linear.…”

Multiplicative Spectral Functionals On

“…With the classical Gleason-Kahane-Żelazko theorem, continuity of φ is not required and is part of the conclusion rather than the assumption. In [3,Section II], the current authors, together with Schulz, made some progress in the case where A is a C -algebra. Amongst a number of results, two of the highlights are stated here as Theorems 1.2 and 1.4.…”

Some character generating functions on Banach algebras

“…That is, under what conditions is a function with multiplicative properties, perhaps involving the spectrum, a character? The problem seems thorny, but some positive results were obtained in [7] and [11].…”