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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.18103 |
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| _version_ | 1866913140606763008 |
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| author | Raickwade, Pavankumar Sivakumar, K. C. |
| author_facet | Raickwade, Pavankumar Sivakumar, K. C. |
| contents | Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive decomposable vectors, is proved. As applications of this result, an alternative proof, as well as an infinite dimensional generalization, of a representation theorem for (i) automorphisms on the completely positive cone and (ii) linear preservers of CP-rank-1 matrices, are presented. It is also shown that if $T$ preserves the set of all decomposable vectors, then so does the Drazin inverse, $T^D$ (if it exists). The case of the Moore-Penrose inverse is also investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18103 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positive Linear Maps on Second Symmetric Product Spaces Raickwade, Pavankumar Sivakumar, K. C. Functional Analysis (2020) Primary 15A69, 15A72, Secondary 46A40 Let $X^{(2)}$ denote the second symmetric product space of a partially ordered vector space $X$, endowed with the projective cone. A characterization of linear maps $T\colon X^{(2)}\to X^{(2)}$ which preserve the set of all positive decomposable vectors, is proved. As applications of this result, an alternative proof, as well as an infinite dimensional generalization, of a representation theorem for (i) automorphisms on the completely positive cone and (ii) linear preservers of CP-rank-1 matrices, are presented. It is also shown that if $T$ preserves the set of all decomposable vectors, then so does the Drazin inverse, $T^D$ (if it exists). The case of the Moore-Penrose inverse is also investigated. |
| title | Positive Linear Maps on Second Symmetric Product Spaces |
| topic | Functional Analysis (2020) Primary 15A69, 15A72, Secondary 46A40 |
| url | https://arxiv.org/abs/2605.18103 |