The set of all effects on a Hilbert space has an affine structure (it is a convex set) as well as a multiplicative structure (it can be equipped with the so-called Jordan triple product). In this paper we describe the corresponding automorphisms of that set. Let H be a complex Hilbert space. Denote by B(H) the C∗-algebra of all bounded linear operators on H. The operator interval [0, I] of all ...

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 ...

Let A be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space A[τ ]. Then A is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of A. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several c...

In a previous paper we showed how the main theorems characterizing operator algebras and operator modules, fit neatly into the framework of the ‘noncommutative Shilov boundary’, and more particularly via the left multiplier operator algebra of an operator space. As well as giving new characterization theorems, the approach of that paper allowed many of the hypotheses of the earlier theorems to ...

We present several examples where moments of creators and annihilators on an interacting Fock space may be realized as moments of creators and annihilators on a full Fock module. Motivated by this experience we answer the question, whether such a possibility exists for arbitrary interacting Fock spaces, in the affirmative sense. We treat the problem in full algebraic generality. As a by-product...

Abstract Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of data, such as documents, syntactic structures, or semantic frames. We present rigorous mathematical framework phrase structure trees and parse context-free grammars (CFG) in Fock space, i.e. infinite-dimensional Hilbert space being used quantum field theory. define novel normal form CFG...

The aim of this paper is to show that if an order preserving bijective transformation of the Hilbert space effect algebra also preserves the probability with respect to a fixed pair of mixed states, then it is an ortho-order automorphism. A similar result for the orthomodular lattice of all sharp effects (i.e., projections) is also presented.

In this note we announce some new methods and results in the theory of nonnormal Hilbert space operators and nonself ad joint operator algebras. A main difficulty in the subject has been the apparent absence of relations between, say, a nonself ad joint algebra of operators and its generated C*-algebra. For example, given full information about the norm-closed algebra P(T) generated by all poly...

We study transitivity conditions on the norm of JB∗-triples, C∗-algebras, JBalgebras, and their preduals. We show that, for the predual X of a JBW∗-triple, each one of the following conditions i) and ii) implies that X is a Hilbert space. i) The closed unit ball of X has some extreme point and the norm of X is convex transitive. ii) The set of all extreme points of the closed unit ball of X is ...