Implications of Extended (A, m)-Isometries

This paper aims to generalize the concept of -isometry to Hilbert spaces and explore new properties of these operators. We introduce new definitions such as -isometries and fractional isometries, and study their spectral and dynamical properties. In addition, we investigate the relationship between these operators and other concepts in operator theory, such as -algebras and representation theory. We also present potential applications in signal processing and quantum mechanics.