标题： 广义Brègman相对熵：简要介绍 显示英文标题

标题： Generalised Brègman relative entropies: a brief introduction

摘要： 我们介绍了非自反Banach空间上广义Brègman相对熵的一些基本元素。 利用Banach空间的非线性嵌入与Euler-Legendre函数，这种方法统一了两种关于Brègman相对熵的方法：一种基于自反Banach空间，另一种基于微分几何。 这一构造允许将Brègman相对熵及其相关的几何和算子结构扩展到概率论、量子论和后量子论任意维状态空间。 我们给出了几个之前文献中未考虑过的例子。 显示英文摘要

摘要： 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.