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Information × Registration Number 0221U106649, 0121U111273 , R & D reports Title Operators in infinite-dimensional spaces: the interplay between geometry, algebra and topology popup.stage_title Head Kadets Volodymyr M., Доктор фізико-математичних наук Registration Date 16-12-2021 Organization V.N. Karazin Kharkiv National University popup.description2  Research object – Banach spaces, equivalent metrics and norms, linear and non-linear operators in Banach spaces, spaces of entire functions, linear operators which preserve hyperbolicity, implicit linear non-homogeneous difference equation, polynomial solutions of linear difference and differential equations. The Purpose of work at the current stage is to deepen our knowledge concerning the structure of the set of operators which attain their norms, and to explore this structure from different viewpoints, in different space and operator classes. Further, to gather different areas of research which are conducted simultaneously by different groups of team members, to draw intermediate conclusions and adjust research plans. Research methods – the implementation of properties of spaces, renormalization, topologies and metrics, filters, slices and extreme points. Results: 8 scientific papers have been prepared, 6 of which have been sent to journals (and 2 of them have been accepted for publication) and the remaining 2 have been published as preprints. The following were investigated: the structure of the set of norm-attaining Lipschitz functionals (in particular, the impossibility of constructing Reed’s metrics is proved); implicit linear non-homogeneous difference and differential equations over an integral commutative ring with a non-Archimedean norm; special linear operators which preserve hyperbolicity. A draft of the monograph on the Daugavet equation and its generalization has been written. Product Description popup.authors Vyshnyakova Ganna M Heneralov Mykola V. HEFTER SERHII L. Goncharyk Anna B. ZAVARZINA OLESIA O. Lotarezs Lyana A. Nguen Hien T. Seliutin Dmytro D. popup.nrat_date 2021-12-16 Close