Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME PROPERTIES OF BILINEAR MAPPINGS ON THE TENSOR PRODUCT OF C⁎ -ALGEBRAS

  • Received : 2019.06.05
  • Accepted : 2019.10.28
  • Published : 2019.12.30
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Abstract

Let 𝓐 and 𝓑 be two unital C⁎-algebras and 𝓐 ⊗ 𝓑 be their algebraic tensor product. For two bilinear maps on 𝓐 and 𝓑 with some specific conditions, we derive a bilinear map on 𝓐 ⊗ 𝓑 and study some characteristics. Considering two 𝓐 ⊗ 𝓑 bimodules, a centralizer is also obtained for 𝓐 ⊗ 𝓑 corresponding to the given bilinear maps on 𝓐 and 𝓑. A relationship between orthogonal complements of subspaces of 𝓐 and 𝓑 and their tensor product is also deduced with suitable example.

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