An isomorphism between the completion of an Algebra and its Caratheodory Extension

Isometries for the Caratheodory Metric

Under certain hypothesises, we prove that a map which is an isometry for the Caratheodory infinitesimal metric at a point is an analytic isomorphism onto its image.

与线性空间相容的拓扑之间的典范格同构

The Canonical Lattice Isomorphism between Topologies Compatible with a Linear Space

本文在赋值域的度量完备化为局部紧空间的条件下，建立了有限维向量空间上相容拓扑格与其系数域扩张后的子空间格之间的典范格同构，并据此刻画了线性映射的连续性及豪斯多夫相容拓扑。

On the Riesz dual of ${\bf L^1(μ)}$

In this article, $(X,\, \mathcal{A},\, μ)$ is a measure apace. A classical result establishes a Riesz isomorphism between $L^1(μ)^{\sim}$ and $L^{\infty}(μ)$ in case the measure $μ$ is $σ$-finite. In general, there still is a natural Riesz homomorphism $Φ: L^{\infty}(μ) \to L^1(μ)^{\sim},$ but it may not be injective or surjective. We prove that always the range of $Φ$ is an order dense Riesz subspace of $L^1(μ)^{\sim}$. If $μ$ is semi-finite, then $L^1(μ)^{\sim}$ is a Dedekind completion of $L^{\infty}(μ)$.

与ℓ^p-伪函数相关的交叉乘积函子

Crossed product functors associated to $\ell^p$-pseudofunctions

本文展示ℓ^p-伪函数可用于构造良好的交叉乘积函子，通过引入与作用于Hilbert值ℓ^p空间的算子相关的Banach代数，证明这些代数在同构下等价，从而推广了群情况下的构造。