Tomi Alaste | Searcharxiv

arXiv2013

Semigroup compactifications in terms of filters

We present a study of semigroup compactifications of a semitopological semigroup $S$ using certain filters on $S$. We characterize closed subsemigroups and closed left, right, and two-sided ideals in any semigroup compactification of any semitopological semigroup $S$ in terms of these filters and in terms of ideals of the corresponding $m$-admissible subalgebra of $C(S)$. Furthermore, we characterize those points in any semigroup compactification of $S$ which belong either to the smallest ideal of the semigroup compactification or to the closure of this smallest ideal.

math.GN↗

arXiv2013

Representation of spectrums of $C^{\ast}$-algebras of bounded functions in terms of filters

Let $X$ be a non-empty set and let $\mathcal{F}$ be any $C^{\ast}$-subalgebra of $\ell ^{\infty}(X)$ containing the constant functions. We show that the spectrum of $\mathcal{F}$ can be considered as a space of certain filters determined by $\mathcal{F}$ on $X$. Furthermore, we show that these filters describe the topology of the spectrum of $\mathcal{F}$.

math.GN↗