Analytic theory of crossed -modules and generalized numerical radius inequalities
Journal of Analysis, vol.34, no.4, pp.2363-2385, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 34 Issue: 4
- Publication Date: 2026
- Doi Number: 10.1007/s41478-026-01089-7
- Journal Name: Journal of Analysis
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.2363-2385
- Keywords: -algebra, Crossed Hilbert space, Crossed module, Multiplier algebra, Numerical radius, Operator inequality
- Süleyman Demirel University Affiliated: Yes
Abstract
This study establishes a rigorous bridge between the theory of crossed modules and functional analysis by extending homological structures to the setting of -algebras. We develop a well-defined framework for crossed modules of Banach and -algebras, utilizing the theory of bimultipliers and their isometric relationship with multiplier algebras to ensure analytic consistency. Central to our construction is the introduction of a novel class of multidimensional structures termed crossed Hilbert spaces. By leveraging bounded linear transformations on these spaces, we construct a categorical bridge between operator algebras and crossed modules. As a primary application, we derive significant generalizations of classical numerical radius inequalities. Our results provide a higher-dimensional perspective on the relationship between the numerical radius and the operator norm, extending fundamental inequalities of operator theory to a broader analytic context.