Invariant Subspace Problem for Norm Attaining Operators (European Journal of Pure and Applied Mathematics, 2025)
Our aim is to characterize norm attaining and absolutely norm attaining quasi-∗-paranormal operators and class Ωn operators defined on a separable Hilbert space. We define invariant non trivial subspaces for the con- sidered operators and we give a matrix representation under certain condition. Compacity, reduisant subspaces and the normality of such operators are also established.
Keywords: Quasi-∗-paranormal operators, Invariant subspaces, Norm attaining operators, Absolutely norm attaining operator; fractional derivatives; differential equations; fractional differential equations; antiperiodic; nonlocal boundary conditions; existence.