A remark on multiplicative linear functionals on measure algebras

A Remark on Continuity of Positive Linear Functionals on Separable Banach *-Algebras

Using a variation of the Murphy-Varopoulos Theorem, we give a new proof of the following R. J. Loy Theorem: Let A be a separable Banach ∗-algebra with center Z such that ZA has at most countable codimension, then every positive linear functional on A is continuous.

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

Borel measurable functionals on measure algebras

For Φ,Ψ ∈ A′′, define 〈Φ Ψ, λ〉 = 〈Φ, Ψ · λ〉 (λ ∈ A′) , and similarly for ♦. Thus (A′′, ) and (A′′,♦) are Banach algebras each containingA as a closed subalgebra. The Banach algebra A is Arens regular if and ♦ coincide on A′′, and A is strongly Arens irregular if and ♦ coincide only on A. A subspace X of A′ is left-introverted if Φ · λ ∈ X whenever Φ ∈ A′′ and λ ∈ X . There has been a great deal...

6 A remark on manageable multiplicative unitaries ∗

We propose a weaker condition for multiplicative unitary operators related to quantum groups, than the condition of manageability introduced by S.L. Woronowicz. We prove that all the main results of the theory of manageable multiplicative unitaries remain true under this weaker condition. We also show that multiplicative unitaries arising naturally in the construction of some recent examples of...

Multiplicative bijective maps on standard operator algebras