in this paper we define an order structure on the $p$-operator projective tensor product of herz algebras and we show that the canonical isometric isomorphism between $a_p(gtimes h)$ and $a_p(g)widehat{otimes}^p a_p(h)$ is an order isomorphism for amenable groups $g$ and $h$.

We study operator spaces, operator algebras, and operator modules, from the point of view of the ‘noncommutative Shilov boundary’. In this attempt to utilize some ‘noncommutative Choquet theory’, we find that Hilbert C∗−modules and their properties, which we studied earlier in the operator space framework, replace certain topological tools. We introduce certain multiplier operator algebras and ...

We study a process algebra ATP for the description and analysis of systems of timed processes. An important feature of the algebra is that its vocabulary of actions contains a distinguished element . An occurrence of is a time event representing progress of time. The algebra has, apart from standard operators of process algebras like CCS or ACP, a primitive binary unit-delay operator. For two a...

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1 2 , two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge 1 ...

This is the second of three lectures on introduction to vertex operator algebras. In this lecture, we shall continue Professor Dong’s lecture to present more fundamental properties of vertex operator algebras. From the mathematical point of view, a vertex operator algebra formally resembles a Lie algebra because the Jacobi identity is used as one of the main axioms. For the Lie algebra aspect o...

Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y , respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is defined by σπ(A) = {z ∈ σ(A) : |z| = maxw∈σ(A) |w|}, where σ(A) denotes the spectrum of A. Assume that Φ : A → B is a map and the range of Φ contains all operators with rank at most two. It is pr...

The theory of vertex (operator) algebras has developed rapidly in the last few years. These rich algebraic structures provide the proper formulation for the moonshine module construction for the Monster group ([B1-B2], [FLM1], [FLM3]) and also give a lot of new insight into the representation theory of the Virasoro algebra and affine Kac-Moody algebras (see for instance [DL3], [DMZ], [FZ], [W])...

The operator algebras of a new family of relativistic geometric models of the relativistic oscillator [1] are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the generators of a non-unitary representation of the so(1, 2) algebra, except a special case when this algebra becomes the standard one of the non-relativistic h...

We discuss the notion of noncommutative point derivations for operator algebras. We look at the noncommutative point derivations for the quiver algebras, A(Cn) where Cn is the directed graph with n-vertices and n-edges forming a cycle. For the algebras Mn ⊗ A(D) and A(Cn) we classify when non-trivial point derivations can occur. We use the point derivations to show that every derivation on A(Cn...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...