In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately represented in terms of the notion of measure cone and the mixing distance [1], a specification of the novel concept of direction distance [2]. It turns out tha...

Branching bisimilarity on normed Basic Process Algebra (BPA) was claimed to be EXPTIMEhard in previous papers without any explicit proof. Recently it is reminded by Jančar that the claim is not so dependable. In this paper, we develop a new complete proof for EXPTIMEhardness of branching bisimilarity on normed BPA. We also prove the associate regularity problem on normed BPA is PSPACE-hard and ...

Introducing the concept of the normalized duality mapping on normed linear space and normed algebra, we extend the usual definitions of the numerical range from one operator to two operators. In this note we study the convexity of these types of numerical ranges in normed algebras and linear spaces. We establish some Birkhoff-James orthogonality results in terms of the algebra numerical range V...

The search for a semantics for higher-order quantum computation leads naturally to the study of categories of normed cones. In the first part of this paper, we develop the theory of continuous normed cones, and prove some of their basic properties, including a Hahn-Banach style theorem. We then describe two different concrete ∗-autonomous categories of normed cones. The first of these categorie...

For each nite simple group G there is a conjugacy class C G such that each nontrivial element of G generates G together with any of more than 1/10 of the members of C G. Precise asymptotic results are obtained for the probability implicit in this assertion.

In earlier work it was shown that each nonabelian finite simple group G has a conjugacy class C such that, whenever 1 = x ∈G, the probability is greater than 1/10 that G= 〈x, y〉 for a random y ∈ C. Much stronger asymptotic results were also proved. Here we show that, allowing equality, the bound 1/10 can be replaced by 13/42; and, excluding an explicitly listed set of simple groups, the bound 2...