Isometries On Banach Spaces Function Spaces

There is a proof of the classification of plane isometries basing on the so-call three reflections theorem, which uses no linear algebra. Findings demonstrate, An isometry on a (semi-)Riemannian manifold is a diffeomorphism of the manifold into itself so that preserves distances or, equivalently, preserves the Riemannian metric (ie ϕ∗g = g ϕ ∗ g = g …. Studies show, It seems that both isometric and unitary operators on a Hilbert space have the following property: U∗U = I U ∗ U = I (U U is an operator and I I is an identity operator, ∗ ∗ is a binary operation. Data confirms, Isometries of $\mathbb {S}^2$ Ask Question Asked 8 years, 7 months ago Modified 1 year, 9 months ago. These findings regarding Isometries On Banach Spaces Function Spaces provide comprehensive context for understanding this subject.