A note on τ-convergence, τ-convergent algebra and applications

To extract a unital commutative C⁎-algebra from the space of almost convergent sequences, the concept of multiplier is introduced and characterized by τ-convergence. For applications, it is proved that the maximal ideal space τN of τ-convergent algebra Mτ is a compactification of N, which includes βN as a closed subset, and Mτ provides an example of non-C⁎-reflexive C⁎-algebra according to Frank–Manuilov–Troitskyʼs criterion.