We study the vector-valued spectrum $\mathcal {M}_{u,\infty }(B_{\ell _2},B_{\ell _2})$, which is set of non-zero algebra homomorphisms from {A}_u(B_{\ell _2})$ (the uniformly continuous holomorphic functions on $B_{\ell _2}$) to

The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous curve in the space of parameters. The main goal of this paper is to relate the asymptotic bound to phase diagrams of quantum statistical mechanical systems. We f...

For various series of complex semi-simple Lie algebras g(t) equipped with irreducible representations V (t), we decompose the tensor powers of V (t) into irreducible factors in a uniform manner, using a tool we call diagram induction. In particular, we interpret the decompostion formulas of Deligne [4] and Vogel [23] for decomposing g respectively for the exceptional series and k ≤ 4 and all si...

In this paper we survey some recent developments in duality for lattices with additional operations paying special attention to Heyting algebras and the connections to Esakia’s work in this area. In the process we analyse the Heyting implication in the setting of canonical extensions both as a property of the lattice and as an additional operation. We describe Stone duality as derived from cano...

S. Sherman has shown [4] that if the self adjoint elements of a C* algebra form a lattice under their natural ordering the algebra is necessarily commutative. In this note we extend this result to real Banach algebras with an identity and arbitrary Banach * algebras with an identity. The central fact for a real Banach algebra A is that if the positive cone is defined to be the uniform closure o...

Some aspects of the theory of Boolean algebras and distributive lattices -in particular, the Stone Representation Theorems and the properties of filters and ideals -are analyzed in a constructive setting.

In  cite{GL}, B. Gerla and I. Leuc{s}tean introduced the notion of similarity on MV-algebra. A similarity MV-algebra is an MV-algebra endowed with a binary operation $S$ that verifies certain additional properties. Also, Chirtec{s} in cite{C}, study the notion of similarity on L ukasiewicz-Moisil algebras. In particular, strong similarity L ukasiewicz-Moisil algebras were defined. In this paper...

This represents a new and more comprehensive approach to the autonomous categories constructed in the monograph [Barr, 1979]. The main tool in the new approach is the Chu construction. The main conclusion is that the category of separated extensional Chu objects for certain kinds of equational categories is equivalent to two usually distinct subcategories of the categories of uniform algebras o...