A Review Note on the Applications of Linear Operators in Hilbert Space

Abstract

Hilbert Spaces are the closest generalization to infinite dimensional spaces of the Euclidean Spaces. We Consider Linear transformations defined in a normed space and we see that all of them are Continuous if the Space is finite Dimensional Hilbert Space Provide a user-friendly framework for the study of a wide range of subjects from Fourier Analysis to Quantum Mechanics. The adjoint of an Operator is defined and the basic properties of the adjoint operation are established. This allows the introduction of self Adjoint Operators are the subject of the section.