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A note on
positive bilinear maps
Aaron C. H. Davey, Cristian Ivanescu and Adi Tcaciuc |
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Vol. 16 (2023), No. 4, 579–590
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Abstract |
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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 -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. |
Keywords
positive maps, multilinear maps, completely bounded,
C$^*$-algebras, positive bilinear maps, positive elements
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Mathematical Subject Classification
Primary: 15A69, 47B65, 47C15, 46L05, 46L07
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Milestones
Received: 2 October 2021
Revised: 12 November 2021
Accepted: 18 August 2022
Published: 31 October 2023
Communicated by Kenneth S. Berenhaut
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Authors |
| Aaron C. H. Davey | |
| Department of Mathematics and
Statistics MacEwan University Edmonton, AB Canada |
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| Cristian Ivanescu | |
| Department of Mathematics and
Statistics MacEwan University Edmonton, AB Canada |
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| Adi Tcaciuc | |
| Department of Mathematics and
Statistics MacEwan University Edmonton, AB Canada |
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| © 2023 MSP (Mathematical Sciences Publishers). |
