Publications of the Research Institute for Mathematical Sciences


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Volume 28, Issue 3, 1992, pp. 455–494
DOI: 10.2977/prims/1195168433

Published online: 1992-06-30

On Algebraic #-Cones In Topological Tensor-Algebras, I Basic Properties and Normality

Gerald Hofmann[1]

(1) HTWK Leipzig, Germany

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.

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Hofmann Gerald: On Algebraic #-Cones In Topological Tensor-Algebras, I Basic Properties and Normality. Publ. Res. Inst. Math. Sci. 28 (1992), 455-494. doi: 10.2977/prims/1195168433