Naslov (srp)

Subnormal operators: a multivariable operator theory perspective

Autor

Stanković, Hranislav, 1994-

Doprinosi

Cvetković Ilić, Dragana, 1977-
Rakočević, Vladimir, 1953-
Marinković, Slađana D., 1963-
Pavlović, Vladimir, 1976-
Nikolov-Radenović, Jovana, 1986-

Opis (srp)

This dissertation presents different new results regarding subnormaloperators using tools and techniques from multivariable operatortheory. It explores the relationship between subnormality andquasinormality and demonstrates that the subnormal n-th roots of aquasinormal operator must also be quasinormal. The study providessufficient conditions under which matricial and sphericalquasinormality of operator pairs are equivalent to the matricial andspherical quasinormality of their n-th powers. It also addresses theconverse of Fuglede Theorem, establishing when subnormal operatorsmust be normal provided their product is normal. The study introducesthe spherical mean transform, examining its spectral properties and itsrole in preserving p-hyponormality.In the context of subnormal operators and subnormal duals, thedissertation addresses the completion of upper-triangular operatormatrices to normality through normal complements. It establishescharacterizations, explores joint spectral properties, and connects theseconcepts to subnormal duals and Aluthge and Duggal transforms.The dissertation also delves into various classes of operators related tonormal and subnormal operators, introducing new concepts andaddressing solvability of operator equations. Additionally, itinvestigates inequalities related to the q-numerical radius, extendingestablished equalities concerning the numerical radius.

Opis (srp)

Bibliography: p. 129-141Biography: p. 143-144 Datum odbrane: 4.7.2024. Mathematical analysis, Functional Analysis

Jezik

srpski

Datum

2024

Licenca

Ovo delo je licencirano pod uslovima licence
Creative Commons CC BY-NC-ND 3.0 AT - Creative Commons Autorstvo - Nekomercijalno - Bez prerada 3.0 Austria License.

http://creativecommons.org/licenses/by-nc-nd/3.0/at/legalcode