Inequalities for the Euclidean operator radius of n-tuple operators and operator matrices in Hilbert C-Modules
| dc.contributor.author | Rashid,Mohammad H.M. | |
| dc.contributor.author | Salameh,Wael Mahmoud Mohammad | |
| dc.date.accessioned | 2024-06-03T12:29:45Z | |
| dc.date.available | 2024-06-03T12:29:45Z | |
| dc.date.issued | 2024-05-15 | |
| dc.description | In functional analysis, particularly in the context of operator theory, the Euclidean operator radius refers to the supremum (least upper bound) of the norms of operators acting on a Hilbert space. If we have a bounded linear operator T on a Hilbert space ℋ𝐻, then its norm is defined as ∥𝑇∥=sup∥𝑥∥=1∥𝑇𝑥∥𝑇=sup𝑥=1𝑇𝑥, where ∥𝑥∥𝑥 denotes the norm of the vector x in the Hilbert space. The Euclidean operator radius extends this concept to a tuple of operators or matrices. | |
| dc.description.abstract | This study takes a detailed look at various inequalities related to the Euclidean operator radius. It examines groups of n-tuple operators, studying how they add up and multiply together. It also uncovers a unique power inequality specific to the Euclidean operator radius. The research broadens its scope to analyze how n-tuple operators, when used as parts of 2×2 operator matrices, illustrate inequalities connected to the Euclidean operator radius. By using the Euclidean numerical radius and Euclidean operator norm for n-tuple operators, the study introduces a range of new inequalities. These inequalities not only set limits for the addition, multiplication, and Euclidean numerical radius of n-tuple operators but also help in establishing inequalities for the Euclidean operator radius. This process involves carefully examining the Euclidean numerical radius inequalities of 2×2 operator matrices with n-tuple operators. Additionally, a new inequality is derived, focusing specifically on the Euclidean operator norm of 2×2 operator matrices. Throughout, the research keeps circling back to the idea of finding and understanding symmetries in linear operators and matrices. The paper highlights the significance of symmetry in mathematics and its impact on various mathematical areas. Keywords: Numerical Radius, Inner Product Space, C∗-Algebra, A-Module | |
| dc.identifier.citation | Rashid, M. H., & Salameh, W. M. M. (2024). Inequalities for the Euclidean Operator Radius of n-Tuple Operators and Operator Matrices in Hilbert C∗-Modules. Symmetry, 16(6), 647. | |
| dc.identifier.doi | https://doi.org/10.3390/sym16060647 | |
| dc.identifier.uri | https://dspace.adu.ac.ae/handle/1/5582 | |
| dc.language.iso | en | |
| dc.publisher | MDPI | |
| dc.title | Inequalities for the Euclidean operator radius of n-tuple operators and operator matrices in Hilbert C-Modules | |
| dc.type | Article |