Tensor products of C(X)-algebras over C(X)

Etienne Blanchard

Tensor products of C(X)-algebras over C(X)

Operator Algebras 2016-09-07 v2

Authors: Etienne Blanchard

Abstract

Given a Hausdorff compact space X, we study the C^*-(semi)-norms on the algebraic tensor product $A\otimes_{alg,C(X)} B$ of two C(X)-algebras A and B over C(X). In particular, if one of the two C(X)-algebras defines a continuous field of C^*-algebras over X, there exist minimal and maximal C^*-norms on $A\otimes_{alg,C(X)} B$ but there does not exist any C^*-norm on $A\otimes_{alg,C(X)} B$ in general.

Keywords

tensor products c(x)-algebras c*-norms compact space continuous fields

Cite

@article{arxiv.math/0012125,
  title  = {Tensor products of C(X)-algebras over C(X)},
  author = {Etienne Blanchard},
  journal= {arXiv preprint arXiv:math/0012125},
  year   = {2016}
}

Comments

8 pages

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