Related papers: Ideals in CB(X) arising from ideals in X

We show that every proper, dense ideal in a C*-algebra is contained in a prime ideal. It follows that a subset generates a C*-algebra as a not necessarily closed ideal if and only if it is not contained in any prime ideal. This allows us to…

Let X be a topological space, and let C(X) be the complex of singular cochains on X with real coefficients. We denote by Cc(X) the subcomplex given by continuous cochains, i.e. by such cochains whose restriction to the space of simplices…

This paper explores the duality between ideals of the ring $B_1(X)$ of all real valued Baire one functions on a topological space $X$ and typical families of zero sets, called $Z_B$-filters, on $X$. As a natural outcome of this study, it is…

Let $\mathscr{B}(X)$ denote the Banach algebra of bounded operators on $X$, where~$X$ is either Tsirelson's Banach space or the Schreier space of order $n$ for some $n\in\mathbb N$. We show that the lattice of closed ideals…

Let $f \colon X \to X$ be a continuous map on a compact metric space $X$ and let $\alpha_f$, $\omega_f$ and $ICT_f$ denote the set of $\alpha$-limit sets, $\omega$-limit sets and nonempty closed internally chain transitive sets…

Given a conditional expectation $P$ from a C*-algebra $B$ onto a C*-subalgebra $A$, we observe that induction of ideals via $P$, together with a map which we call co-induction, forms a Galois connection between the lattices of ideals of $A$…

Let $X$ be a locally compact non compact Hausdorff topological space. Consider the algebras $C(X)$, $C_b(X)$, $C_0(X)$, and $C_{00}(X)$ of respectively arbitrary, bounded, vanishing at infinity, and compactly supported continuous functions…

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive…

In these notes, we give a survey of the main results of [BC] and [BW]. Our aim is to generalize the geometric classification of (one-sided) ideals of the first Weyl algebra $ A_1(C) $ (see [BW1, BW2]) to the ring $ D(X) $ of differential…

The purpose of this paper is to investigate the duality between large scale and small scale. It is done by creating a connection between C*-algebras and scale structures. In the commutative case we consider C*-subalgebras of $C^b(X)$, the…

In these expository notes, intended for students without background in point-set topology, we develop the basic theory of the Stone-Cech compactification without reference to open sets, closed sets, filters, or nets. In particular, this…

In the paper the \v{C}ech border homology and cohomology groups of closed pairs of normal spaces are constructed and investigated. These groups give intrinsic characterizations of \v{C}ech homology and cohomology groups based on finite open…

Let $X$ be a quasi-compact algebraic stack with quasi-finite and separated diagonal. We classify the thick $\otimes$-ideals of $\mathsf{D}_{\mathrm{qc}}(X)^c$. If $X$ is tame, then we also compute the Balmer spectrum of the…

Let $X$ be a zero-dimensional space and $C_c(X)$ be the set of all continuous real valued functions on $X$ with countable image. In this article we denote by $C_c^K(X)$ (resp., $C_{c}^{\psi}(X)$) the set of all functions in $C_c(X)$ with…

We introduce the notion of ideal triangle in the Bruhat-Tits building associated to a split group -- it is analogous to the usual notion of triangle, but one vertex is "at infinity" in a certain direction. We prove that the algebraic…

In this paper, it is shown that the Boolean ring of a commutative ring is isomorphic to the ring of clopens of its prime spectrum. In particular, Stone's Representation Theorem is generalized. The prime spectrum of the Boolean ring of a…

A topological space $X$ is called submaximal if every dense subset of $X$ is open. In this paper, we show that if $\beta X$, the Stone-\v{C}ech compactification of $X$, is a submaximal space, then $X$ is a compact space and hence $\beta…

Let (X,\sigma) be a symplectic space admitting a complex structure and let R(X,\sigma) be the corresponding resolvent algebra, i.e. the C*-algebra generated by the resolvents of selfadjoint operators satisfying canonical commutation…

By a characterization of semiprime $SA$-rings by Birkenmeier, Ghirati and Taherifar in \cite[Theorem 4.4]{B}, and by the topological characterization of $C(X)$ as a Baer-ring by Stone and Nakano in \cite[Theorem 3.25]{KM}, it is easy to see…

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view…