Related papers: Nest algebras in $c_1$

In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras of conjugacy classes of symmetric groups $S_n$ admit a stabilization (in a non-obvious sense) as $n\to \infty$. We extend their construction to a class of pairs of…

We give necessary and sufficient conditions which a graph should satisfy in order for its associated $C^\ast$-algebra to have a $T_1$ primitive ideal space. We give a description of which one-point sets in such a primitive ideal space are…

Let $A$ and $B$ be unital Banach algebras with $A$ a subalgebra of $B$. Denote the algebra of all $n\times n$ matrices with entries from $A$ by $M_{n}(A)$. In this paper we prove some results concerning the open question: If $A$ is inverse…

Let C be an axiomatizable class of order continuous real or complex Banach lattices, that is, this class is closed under isometric vector lattice isomorphisms and ultraproducts, and the complementary class is closed under ultrapowers. We…

Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable…

We identify a class of smooth Banach *-algebras that are differential subalgebras of commutative C*-algebras whose openness of multiplication is completely determined by the topological stable rank of the target C*-algebra. We then show…

We study homological invariants of \'etale groupoids arising from Smale spaces, continuing on our previous work, but going beyond the stably disconnected case by incorporating resolutions in the space direction. We show that the homology…

We define and systematically study nonassociative C*-algebras as C*-algebras internal to a topological tensor category. We also offer a concrete approach to these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded operators…

We define a Banach algebra A to be dual if $A = (A_\ast)^\ast$ for a closed submodule $A_\ast$ of $A^\ast$. The class of dual Banach algebras includes all $W^\ast$-algebras, but also all algebras M(G) for locally compact groups G, all…

Spectral morphisms between Banach algebras are useful for comparing their K-theory and their "noncommutative dimensions" as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral…

Hom-alternative and Hom-Jordan algebras are shown to give rise to Hom-Nambu algebras of arities 2^{k+1} + 1. The class of n-ary Hom-Maltsev algebras is studied. Multiplicative n-ary Hom-Nambu-Lie algebras are shown to be n-ary Hom-Maltsev…

We give a criterion ensuring that the elementary class of a modular Banach space E (that is, the class of Banach spaces, some ultrapower of which is linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m H, where H…

We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix…

We consider tracial stability, which requires that tuples of elements of a C*-algebra with a trace that nearly satisfy the relation are close to tuples that actually satisfy the relation. Here both "near" and "close" are in terms of the…

Nested parentheses are forms in an algebra which define orders of evaluations. A class of well-formed sets of associated opening and closing parentheses is well studied in conjunction with Dyck paths and Catalan numbers. Nested parentheses…

The paper describes homomorphisms between Douglas algebras and some semisimple Banach algebras. The main tool is a result on the structure of the space $C(Z,\mathfrak M)$ of continuous mappings from a connected first-countable $T_1$ space…

We construct dense Banach subalgebras $A$ of the null sequence algebra $c_0$ which are spectral invariant, but do not satisfy the $D_1$-condition $\|ab \|_A \leq K(\|a\|_{\infty} \|b\|_A + \|a \|_A \|b \|_{\infty})$, for all $a, b \in A$.…

In this paper we study the structure of the $C^*$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^*$-algebras over this poset. We construct the extensions…

By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…

This paper has three parts. First, we establish some of the basic model theoretic facts about $M_{\mathcal{T}}$, the Tsirelson space of Figiel and Johnson \cite{FJ}. Second, using the results of the first part, we give some facts about…