weighted convolution measure algebras characterized by convolution algebras

Weighted Convolution Measure Algebras Characterized by Convolution Algebras

The weighted semigroup algebra Mb (S, w) is studied via its identification with Mb (S) together with a weighted algebra product *w so that (Mb (S, w), *) is isometrically isomorphic to (Mb (S), *w). This identification enables us to study the relation between regularity and amenability of Mb (S, w) and Mb (S), and improve some old results from discrete to general case.

A class of weighted convolution Fréchet algebras

For an increasing sequence (ωn) of algebra weights on R + we study various properties of the Fréchet algebra A(ω) = ⋂ n L (ωn) obtained as the intersection of the weighted Banach algebras L(ωn). We show that every endomorphism of A(ω) is standard, if for all n ∈ N there exists m ∈ N such that ωm(t)/ωn(t) → ∞ as t → ∞. Moreover, we characterise the continuous derivations on this algebra: If for ...

Convolution Algebras: Relational Convolution, Generalised Modalities and Incidence Algebras

Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantalevalued functions relative to ternary relations. The resulting notion of relational convolution leads to generalised binary and unary modal operators for qualitative and quantitative models, and to more conventional variants, when ternary ...

Derivations of Convolution Algebras

Second Hochschild Cohomology of Convolution Algebras

Partial Semigroups and Convolution Algebras

Partial Semigroups are relevant to the foundations of quantum mechanics and combinatorics as well as to interval and separation logics. Convolution algebras can be understood either as algebras of generalised binary modalities over ternary Kripke frames, in particular over partial semigroups, or as algebras of quantale-valued functions which are equipped with a convolution-style operation of mu...