The concept of algebraic #-cones (alg-# cones) in topological tensor-algebras _E_⊗[τ] is introduced. It seems to be useful because the well-known cones such as the cone of positivity _E_⊗, the cone of reflection posilivity (Osterwalder-Schrader cone), and some cones of α-positivity in QFT with an indefinite metric are examples of alg-# cones. It is investigated whether or not the known properties of _E_⊗ (e.g., _E_⊗ is a proper and generating cone not satisfying the decomposition property) apply to alg-# cones. For proving deeper results, the structure of the elements of alg-# cones is analyzed, and certain estimations between the homogeneous components of those elements are proven. Using them, a detailed investigation of the normality of alg-# cones is given. Furthermore, the convex hull of finitely many alg-# cones is also considered.
Cite this article
Gerald Hofmann, On Algebraic #-Cones In Topological Tensor-Algebras, I Basic Properties and Normality. Publ. Res. Inst. Math. Sci. 28 (1992), no. 3, pp. 455–494DOI 10.2977/PRIMS/1195168433