The terminology and notation used here are introduced in the following articles: [18], [8], [20], [5], [7], [6], [3], [1], [17], [13], [19], [14], [2], [4], [15], [10], [11], [9], and [12]. One can prove the following propositions: (1) Let X, Y , Z be complex linear spaces, f be a linear operator from X into Y , and g be a linear operator from Y into Z. Then g · f is a linear operator from X in...

In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C∗-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C∗-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yi...

An extension of bornological algebras with a bounded linear section gives rise to a six term exact sequence of the associated periodic and entire cyclic cohomology groups. 1. Introduction A convex vector bornology on a vector space is a collection of subsets satisfying some conditions 8]. A typical example is the collection of bounded subsets of a locally convex vector space. A bornological alg...

We provide a direct proof that the Haagerup estimate on the completely bounded norm of elementary operators is best possible in the case of B(H) via a generalisation of a theorem of Stampfli. We show that for an elementary operator T of length `, the completely bounded norm is equal to the k-norm for k = `. A C*-algebra A has the property that the completely bounded norm of every elementary ope...

We consider the problem of identifying boundary values of holomorphic functions on (non-smooth) bounded domains in C 2 with boundaries that are Levi-at oo of a small set. Assuming also that the domain is circular, we construct a type of extension operator from the algebra of bounded holomorphic functions on a leaf of the induced Levi-foliation to the algebra of bounded holomorphic functions on ...

The papers [21], [8], [23], [25], [24], [5], [7], [6], [19], [4], [1], [2], [18], [10], [22], [13], [3], [20], [16], [15], [9], [12], [11], [14], and [17] provide the terminology and notation for this paper. Let X be a non empty set and let f , g be elements of X . Then g · f is an element of X . One can prove the following propositions: (1) Let X, Y , Z be real linear spaces, f be a linear ope...

Stone algebras have been characterized by Chen and Grätzer in terms of triples (B;D;'), whereD is a distributive lattice with 1; B is a Boolean algebra, and ' is a bounded lattice homomorphism from B into the lattice of …lters of D: If D is bounded, the construction of these characterizing triples is much simpler, since the homomorphism ' can be replaced by one from B into D itself. The triple ...

$-calculus is a higher-order polyadic process algebra with a utility (cost) integrating deliberative and reactive approaches for action selection in real time, and allowing to capture bounded optimization and metaresoning in distributed interactive AI systems. In this paper we present basic notions of $-calculus and demonstrate the versatility of its k meta-control to plan behaviors for single ...

In this paper we give some characterizations of M. Hamana’s injective envelope I(A) of a C∗-algebra A in the setting of operator spaces and completely bounded maps. These characterizations lead to simplifications and generalizations of some known results concerning completely bounded projections onto C∗-algebras. We prove that I(A) is rigid for completely bounded A-module maps. This rigidity yi...

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal.