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http://dx.doi.org/10.11568/kjm.2019.27.4.977

SOME PROPERTIES OF BILINEAR MAPPINGS ON THE TENSOR PRODUCT OF C⁎ -ALGEBRAS  

Sarma, Anamika (Department of Mathematics Gauhati University)
Goswami, Nilakshi (Department of Mathematics Gauhati University)
Mishra, Vishnu Narayan (Department of Mathematics Indira Gandhi National Tribal University)
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 977-1003 More about this Journal
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.
Keywords
bilinear map; $C^{\ast}$-algebra; centralizer; orthogonal complement; tensor product;
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