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

To extract a unital commutative C ⁎ -algebra from the space l a c ∞ ( N , C ) 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 τ N of τ-convergent algebra M τ is a compactification of N , which includes β N as a closed subset, and M τ provides an example of non- C ⁎ -reflexive C ⁎ -algebra according to Frank–Manuilov–Troitskyʼs criterion.