A note on positive bilinear maps

dc.contributor.author	Davey, Aaron C. H.
dc.contributor.author	Ivanescu, Cristian
dc.contributor.author	Tcaciuc, Adi
dc.date.accessioned	2025-06-13T15:09:45Z
dc.date.available	2025-06-13T15:09:45Z
dc.date.issued	2023
dc.description.abstract	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.
dc.identifier.citation	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
dc.identifier.doi	https://doi.org/10.2140/involve.2023.16.579
dc.identifier.uri	https://hdl.handle.net/20.500.14078/3975
dc.language.iso	en
dc.rights	All Rights Reserved
dc.subject	C∗-algebras
dc.subject	multilinear
dc.subject	2-positive
dc.subject	bounded bilinear maps
dc.subject	bounded linear maps
dc.subject	correspondence
dc.title	A note on positive bilinear maps	en
dc.type	Article Post-Print

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