Weak multiplicative operators on function algebras without units

Weak C-Hopf Algebras and Multiplicative Isometries

We show how the data of a finite dimensional weak C∗-Hopf algebra can be encoded into a pair (H, V ) where H is a finite dimensional Hilbert space and V :H⊗H → H⊗H is a partial isometry satisfying, among others, the pentagon equation. In case of V being unitary we recover the Baaj-Skandalis multiplicative unitary of the discrete compact type. Relation to the pseudomultiplicative unitary approac...

Multiplicative bijective maps on standard operator algebras

Martin Frontal operators in weak Heyting algebras

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation τ(a) ≤ b ∨ (b → a), for all a, b ∈ A. These operators were studied from an algebraic, logical an...

Weakly multiplicative coactions of quantized function algebras

A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the subalgebra of coinvariants) is obtained for such coactions of a cosemisimple Hopf algebra. This is applied for two coactions α, β : A → A⊗O, where A is the co...

Strong Ditkin Algebras without Bounded Relative Units

In a previous note the author gave an example of a strong Ditkin algebra which does not have bounded relative units in the sense of Dales. In this note we investigate a certain family of Banach function algebras on the one point compactification of N, and see that within this family are many easier examples of strong Ditkin algebras without bounded relative units in the sense of Dales.