A Hölder type inequality and an interpolation theorem in Euclidean Jordan algebras
| dc.contributor.author | Gowda, Muddappa Seetharama | |
| dc.date.accessioned | 2018-10-23T15:09:07Z | |
| dc.date.available | 2018-10-23T15:09:07Z | |
| dc.date.issued | 2018-09-14 | |
| dc.description.abstract | In a Euclidean Jordan algebra V of rank n which carries the trace inner product, to each element x we associate the eigenvalue vector λ(x) whose components are the eigenvalues of x written in the decreasing order. For any p ∈ [1,∞], we define the spectral p-norm of x to be the p-norm of λ(x) in Rⁿ. In this paper, we show that ||x ◦ y||1 ≤ ||x|| ||y||q, where x ◦ y denotes the Jordan product of two elements x and y in V and q is the conjugate of p. For a linear transformation on V, we state and prove an interpolation theorem relative to these spectral norms. In addition, we compute/estimate the norms of Lyapunov transformations, quadratic representations, and positive transformations on V. | en_US |
| dc.description.uri | https://arxiv.org/abs/1809.05417 | en_US |
| dc.format.extent | 20 pages | en_US |
| dc.genre | journal article pre-print | en_US |
| dc.identifier | doi:10.13016/M2736M576 | |
| dc.identifier.uri | http://hdl.handle.net/11603/11654 | |
| dc.language.iso | en_US | en_US |
| dc.relation.isAvailableAt | The University of Maryland, Baltimore County (UMBC) | |
| dc.relation.ispartof | UMBC Mathematics Department Collection | |
| dc.relation.ispartof | UMBC Faculty Collection | |
| dc.rights | This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author. | |
| dc.subject | Euclidean Jordan algebra | en_US |
| dc.subject | H¨older type inequality | en_US |
| dc.subject | strong operator commutativity | en_US |
| dc.subject | majorization | en_US |
| dc.subject | Schur-convexity | en_US |
| dc.subject | positive transformation | en_US |
| dc.subject | interpolation theorem | en_US |
| dc.title | A Hölder type inequality and an interpolation theorem in Euclidean Jordan algebras | en_US |
| dc.type | Text | en_US |