2000 character limit reached
Generalised Brègman relative entropies: a brief introduction (2306.02412v3)
Published 4 Jun 2023 in math-ph, cs.IT, math.IT, and math.MP
Abstract: We present some basic elements of the theory of generalised Br`{e}gman relative entropies over nonreflexive Banach spaces. Using nonlinear embeddings of Banach spaces together with the Euler--Legendre functions, this approach unifies two former approaches to Br`{e}gman relative entropy: one based on reflexive Banach spaces, another based on differential geometry. This construction allows to extend Br`{e}gman relative entropies, and related geometric and operator structures, to arbitrary-dimensional state spaces of probability, quantum, and postquantum theory. We give several examples, not considered previously in the literature.