Hadamard's lemma in separable Hilbert spaces

TL;DR

This paper extends Hadamard's Lemma to the context of separable Hilbert spaces, broadening its applicability in functional analysis and operator theory.

Contribution

It introduces a generalized version of Hadamard's Lemma specifically tailored for separable Hilbert spaces, which was not previously established.

Findings

Generalization of Hadamard's Lemma to separable Hilbert spaces

Potential applications in operator theory and functional analysis

Foundation for further theoretical developments in Hilbert space analysis

Abstract

We extend Hadamard's Lemma to the setting of a separable Hilbert space.