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Minimal incomplete norms on Banach algebras

Michael Meyer (1992)

Studia Mathematica

We study the family of all not necessarily complete algebra norms on a semisimple Banach algebra as a partially ordered set and investigate the existence and properties of minimal elements.

Module maps over locally compact quantum groups

Zhiguo Hu, Matthias Neufang, Zhong-Jin Ruan (2012)

Studia Mathematica

We study locally compact quantum groups and their module maps through a general Banach algebra approach. As applications, we obtain various characterizations of compactness and discreteness, which in particular generalize a result by Lau (1978) and recover another one by Runde (2008). Properties of module maps on L ( ) are used to characterize strong Arens irregularity of L₁() and are linked to commutation relations over with several double commutant theorems established. We prove the quantum group...

Multiplicative functionals and entire functions

Krzysztof Jarosz (1996)

Studia Mathematica

Let A be a complex Banach algebra with a unit e, let T, φ be continuous functionals, where T is linear, and let F be a nonlinear entire function. If T ∘ F = F ∘ φ and T(e) = 1 then T is multiplicative.

Multiplicative functionals and entire functions, II

Krzysztof Jarosz (1997)

Studia Mathematica

Let A be a complex Banach algebra with a unit e, let F be a nonconstant entire function, and let T be a linear functional with T(e)=1 and such that T∘F: A → ℂ is nonsurjective. Then T is multiplicative.

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