Research Projects

The text introduces the concept of operator shifts and discusses basic properties of operators on directed trees. It motivates the study of graph theoretical geometrics on Hilbert space and explores analytical and dynamical structures of certain operators on directed trees. The dynamics of operators on directed tress are introduced, and enlarging their dynamical behavior is beneficial. The text also explores the structure of invariant directed graphs under different classes of operators, such as weighted shifts and multiplication operators. It also discusses multivariate operator theory, specifically the algebraic structure of operator shifts and the nature of multiplication operators on directed trees. The text also discusses the dynamics of weight shift operators on directed trees.