د.ابراهيم محمد حسن2026-06-102026-06-10https://dspace.academy.edu.ly/handle/123456789/2270When considering linear operators on normed vector spaces, one often in encounters the notion of norm (Denoted generally by‖∙‖); hence, one can speak of the norm of an operator. As this norm may be finite or infinite, linear operators are classified as being bounded or unbounded depending on whether their norm is finite or infinite, respectively.In this dissertation, we consider the spectral theory of bounded self-adjoint operators on certain Banach spaces. In particular, we present standard results about the generic behavior of the spectrum of this class of operators on Hilbert spaces. We also consider the basic ideas of linear operators and linear functional on finite dimensional spaces, Hilbert-adjoint operators, and convergence of sequences of linear operator. Very special topics in the study of the spectral of bounded self-adjoint linear operators especially are also considered. These include spectral properties and spectral representation of bounded self-adjoint linear operators.SPECTRAL OF BOUNDED SELF-