Relations between Banach function algebras and their uniform closures

Surjective Real-Linear Uniform Isometries Between Complex Function Algebras

In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$,  where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T...

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras

Uniform Closure of Dual Banach Algebras

We give a characterization of the ”uniform closure” of the dual of a C-algebra. Some applications in harmonic analysis are given. 1. Four topologies on the unit ball of a C-algebra Let A be a C-algebra and P (A),S(A),A1, and A denote the pure state space, state space, closed dual unit ball, and the dual of A, respectively, all equipt with the w-topology. Let A1denote the closed unit ball of A. ...

Heisenberg–Lie commutation relations in Banach algebras

Given q1, q2 ∈ C \ {0}, we construct a unital Banach algebra Bq1,q2 which contains a universal normalized solution to the (q1, q2)-deformed Heisenberg–Lie commutation relations in the following specific sense: (i) Bq1,q2 contains elements b1, b2, and b3 which satisfy the (q1, q2)-deformed Heisenberg–Lie commutation relations (that is, b1b2 − q1b2b1 = b3, q2b1b3 − b3b1 = 0, and b2b3 − q2b3b2 = 0...

Weak * Sequential Closures in Banach Space Theory and Their Applications

Let X be a (real or complex) Banach space, its dual Banach space will be denoted by X *. We use standard notation and terminology of Banach space theory, see J.Lindenstrauss and L.Tzafriri [LT]. By a subspace we mean a linear, but not necessarily closed, subspace. We also assume some knowledge of general topology and ordinal numbers, see P.S.Aleksandrov[A]. Definition 1.1. Let A be a subset of ...