Subnormalni operatori: pristup višedimenzionalne teorije operatora

[H. Stanković]

IX, 150, IX, 42 str.

Bibliography: p. 129-141 Biography: p. 143-144

Mathematical analysis, Functional Analysis

This dissertation presents different new results regarding subnormal operators using tools and techniques from multivariable operator theory. It explores the relationship between subnormality and quasinormality and demonstrates that the subnormal n-th roots of a quasinormal operator must also be quasinormal. The study provides sufficient conditions under which matricial and spherical quasinormality of operator pairs are equivalent to the matricial and spherical quasinormality of their n-th powers. It also addresses the converse of Fuglede Theorem, establishing when subnormal operators must be normal provided their product is normal. The study introduces the spherical mean transform, examining its spectral properties and its role in preserving p-hyponormality. In the context of subnormal operators and subnormal duals, the dissertation addresses the completion of upper-triangular operator matrices to normality through normal complements. It establishes characterizations, explores joint spectral properties, and connects these concepts to subnormal duals and Aluthge and Duggal transforms. The dissertation also delves into various classes of operators related to normal and subnormal operators, introducing new concepts and addressing solvability of operator equations. Additionally, it investigates inequalities related to the q-numerical radius, extending established equalities concerning the numerical radius.

subnormalni operatori, kvazinormalni operatori, normalni operatori, višedimenzionalna teorija operatora, kompletiranje do normalnosti, sferična srednja transformacija

subnormal operators, quasinormal operators, normal operators, multivariable operator theory, completion to normality, spherical mean transform

517.983/.986(043.3)

P140

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