Related papers: Nest Representations of TAF Algebras

In this paper we study the nest representations of a strongly maximal TAF algebra, whose ranges contain non-zero compact operators. We introduce a particular class of such representations, the essential nest representations, and we show…

In this paper we give a criterion for an ideal of a TAF algebra to be meet irreducible. We show that an ideal $J$ of $A$ is meet irreducile if and only if the C$^*$-envelope of the quotient $A/J$ is primitive. In that case, A/J admits a…

This paper is a comprehensive study of the nest representations for the free semigroupoid algebra $\flgee$ of countable directed graph $G$ as well as its norm-closed counterpart, the tensor algebra $\T^{+}(G)$. We prove that the finite…

A set of meet-irreducible ideals is described for a class of maximal triangular almost finite algebras. This set forms a topological space under the hull-kernel closure, and there is a one-to-one correspondence between closed sets in this…

We introduce a class of left ideals (and subalgebras) of nest algebras determined by totally ordered families of partial isometries on a complex Hilbert space $H$. Let $\mathcal{E}$ be a family of partial isometries that is totally ordered…

Let $\mathcal{A}$ be an operator algebra on a Hilbert space. We say that an element $G\in {\mathcal{A}}$ is an all-derivable point of ${\mathcal{A}}$ if every derivable linear mapping $\phi$ at $G$ (i.e. $\phi(ST)=\phi(S)T+S\phi(T)$ for any…

We show that the family of nest algebras with $r$ non-zero nest projections is stable, in the sense that an approximate containment of one such algebra within another is close to an exact containment. We use this result to give a local…

We show that the class of representable substitution algebras is characterized by a set of universal first order sentences. In addition, it is shown that a necessary and sufficient condition for a substitution algebra to be representable is…

A Dirichlet operator algebra is a nonself-adjoint operator algebra $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ is norm-dense in the C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions,…

Let ${\mathcal N}$ and ${\mathcal M}$ be nests on Banach spaces $X$ and $Y$ over the (real or complex) field $\mathbb F$ and let $\mbox{\rm Alg}{\mathcal N}$ and $\mbox{\rm Alg}{\mathcal M}$ be the associated nest algebras, respectively. It…

Let k be an algebraically closed field and A be a finite-dimensional associative basic k-algebra of the form A=kQ/I where Q is a quiver without oriented cycles or double arrows and I is an admissible ideal of kQ. We consider roots of the…

Suppose that $\mathscr{A}$ is an operator algebra on a Hilbert space $H$. An element $V$ in $\mathscr{A}$ is called an all-derivable point of $\mathscr{A}$ for the strong operator topology if every strong operator topology continuous…

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.

We give a necessary and sufficient criterion for an operator in a nest algebra to belong to a proper two-sided ideal of that algebra. Using this result, we describe the strong radical of a nest algebra, and give a general description of the…

(1) Let 1\leq k\leq \omega. Call an atom structure \alpha weakly k neat representable, the term algebra is in \RCA_n\cap \Nr_n\CA_{n+k}, but the complex algebra is not representable. Call an atom structure neat if there is an atomic algebra…

Let W be an associative PI algebra over a field F of characteristic zero, graded by a finite group G. Let id_{G}(W) denote the T-ideal of G-graded identities of W. We prove: 1. {[G-graded PI equivalence]} There exists a field extension K of…

We classify $n$-representation infinite algebras $\Lambda$ of type \~A. This type is defined by requiring that $\Lambda$ has higher preprojective algebra $\Pi_{n+1}(\Lambda) \simeq k[x_1, \ldots, x_{n+1}] \ast G$, where $G \leq…

Let $G$ be a real Lie group with Lie algebra $\mathfrak g$. Given a unitary representation $\pi$ of $G$, one obtains by differentiation a representation $d\pi$ of $\mathfrak g$ by unbounded, skew-adjoint operators. Representations of…

Let ${\mathcal N}$ be a nest on a complex Banach space $X$ and let $\mbox{ Alg}{\mathcal N}$ be the associated nest algebra. We say that an operator $Z\in \mbox{ Alg}{\mathcal N}$ is an all-derivable point of $\mbox{ Alg}{\mathcal N}$ if…

We define the representation dimension of an algebraic torus $T$ to be the minimal positive integer $r$ such that there exists a faithful embedding $T \hookrightarrow \operatorname{GL}_r$. Given a positive integer $n$, there exists a…