Maps Completely Preserving the Quadratic Operators
Let $\mathcal{A}$ and $\mathcal{B}$ be standard operator algebras on Banach spaces $\mathcal{X}$ and $\mathcal{Y}$, respectively. Let $\phi: \mathcal{A} \rightarrow \mathcal{B}$ be a bijective map. In this paper, we show that $\phi$ is completely preserving quadratic operator in both directions if a...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2023-03-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_701631_79f8d40ea60b10f296d7bf29833a17b5.pdf |
| _version_ | 1797666553881165824 |
|---|---|
| author | Roja Hosseinzadeh |
| author_facet | Roja Hosseinzadeh |
| author_sort | Roja Hosseinzadeh |
| collection | DOAJ |
| description | Let $\mathcal{A}$ and $\mathcal{B}$ be standard operator algebras on Banach spaces $\mathcal{X}$ and $\mathcal{Y}$, respectively. Let $\phi: \mathcal{A} \rightarrow \mathcal{B}$ be a bijective map. In this paper, we show that $\phi$ is completely preserving quadratic operator in both directions if and only if $\phi$ is 2-quadratic preserving operator in both directions and if and only if $\phi$ is either an isomorphism or (in the complex case) a conjugate isomorphism. |
| first_indexed | 2024-03-11T20:00:04Z |
| format | Article |
| id | doaj.art-061a47ac60aa4e21a88b449716ccc7b2 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-03-11T20:00:04Z |
| publishDate | 2023-03-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-061a47ac60aa4e21a88b449716ccc7b22023-10-04T08:29:36ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002023-03-0120212313210.22130/scma.2022.522940.901701631Maps Completely Preserving the Quadratic OperatorsRoja Hosseinzadeh0Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran.Let $\mathcal{A}$ and $\mathcal{B}$ be standard operator algebras on Banach spaces $\mathcal{X}$ and $\mathcal{Y}$, respectively. Let $\phi: \mathcal{A} \rightarrow \mathcal{B}$ be a bijective map. In this paper, we show that $\phi$ is completely preserving quadratic operator in both directions if and only if $\phi$ is 2-quadratic preserving operator in both directions and if and only if $\phi$ is either an isomorphism or (in the complex case) a conjugate isomorphism.https://scma.maragheh.ac.ir/article_701631_79f8d40ea60b10f296d7bf29833a17b5.pdfpreserving problemcompletely preserving problemquadratic operatoroperator algebra |
| spellingShingle | Roja Hosseinzadeh Maps Completely Preserving the Quadratic Operators Sahand Communications in Mathematical Analysis preserving problem completely preserving problem quadratic operator operator algebra |
| title | Maps Completely Preserving the Quadratic Operators |
| title_full | Maps Completely Preserving the Quadratic Operators |
| title_fullStr | Maps Completely Preserving the Quadratic Operators |
| title_full_unstemmed | Maps Completely Preserving the Quadratic Operators |
| title_short | Maps Completely Preserving the Quadratic Operators |
| title_sort | maps completely preserving the quadratic operators |
| topic | preserving problem completely preserving problem quadratic operator operator algebra |
| url | https://scma.maragheh.ac.ir/article_701631_79f8d40ea60b10f296d7bf29833a17b5.pdf |
| work_keys_str_mv | AT rojahosseinzadeh mapscompletelypreservingthequadraticoperators |