The C*-algebra of bounded operators on the separable Hilbert space cannot be mapped to a W*-algebra in such a way that each unital commutative C*-subalgebra C(X) factors normally through `∞(X). Consequently, there is no faithful functor discretizing C*-algebras to W*-algebras this way.

We prove that a bounded stack can be specified in process algebra with just the operators alternative and sequential composition and iteration. The bounded bag cannot be specified with these operators, but can be specified if we add the parallel composition operator without communication (free merge). The bounded queue cannot even be specified in this signature; we need a form of variable bindi...

Let G be a locally compact σ-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra A(G) of G. We characterise the completely bounded multidimensional multipliers associated with A(G) in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all n-dimensional compl...

We determine the extended eigenvalues and extended eigenvectors of weighted shifts. We also describe the structure of Deddens algebras and spectral radius algebras associated to weighted shifts. In particular, we show that these algebras are weakly dense in the algebra of all bounded linear operators or in the algebra of lower triangular operators.

In this paper, we introduce a class of infinite matrices related to the Beurling algebra of periodic functions, and we show that it is an inverse-closed subalgebra of B(`w), the algebra of all bounded linear operators on the weighted sequence space `w, for any 1 ≤ q <∞ and any discrete Muckenhoupt Aq-weight w. Constructive Approximation, To appear

Pseudo-BCK algebras were introduced by G. Georgescu and A. Iorgulescu as a generalization of BCK algebras in order to give a corresponding structure to pseudo-MV algebras, since the bounded commutative BCK algebras corresponde to MV algebras. Properties of pseudo-BCK algebras and their connections with other fuzzy structures were established by A. Iorgulescu and J. Kühr. The aim of this paper i...

Effect algebras are the main object of study in quantum mechanics. Module measures those defined on an effect algebra with values a topological module. Let R be ring and M R-module. L algebra. The range module measure ?:L?M is studied. Among other results, we prove that if sRDP ?-effect natural basis ?:L?R countably additive measure, then ? has bounded variation.

Let AI, be commutative semlslmple Banach algebras and 1 02 A2 be their projective tensor product. We prove that, if 10 2 is a group algebra (measure algebra) of a locally compact abelian group, then so are A 1 and A2. As a consequence, we prove that, if G is a locally compact abelian group and A is a comutatlve semi-simple Banach algebra, then the Banach algebra LI(G,A) of A-valued Bochner inte...

Let A be a Banach algebra with a bounded left approximate identity. The Cohen Factorization Theorem is used to prove several results concerning the representation theory of A.

It is proved that bounded linear operators on Banach spaces of “cadlag” functions are measurable with respect to the Borel σ-algebra associated with the Skorokhod topology.