A note on positive bilinear maps
Faculty Advisor
Date
2023
Keywords
C∗-algebras, multilinear, 2-positive, bounded bilinear maps, bounded linear maps, correspondence
Abstract (summary)
This paper concerns positive maps between C∗-algebras, particularly when those positive maps are multilinear. We construct examples of positive bilinear maps that are not 2-positive, and therefore are not completely positive bilinear maps. Paulsen and Smith showed that completely bounded bilinear maps are in one-to-one correspondence with completely bounded linear maps. We show that a similar correspondence does not hold for positive bilinear and linear maps. In particular, we observe that a similar correspondence does not hold if we replace completely bounded with completely positive.
Publication Information
Davey, A. C. H., Ivanescu, C., & Tcaciuc, A. (2023). A note on positive bilinear maps. Involve, 16(4), 579–590. https://doi.org/10.2140/involve.2023.16.579
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Article Post-Print
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