K*-代数与对偶
K*-algebras and duality
摘要：
本论文是我的博士论文（在俄罗斯获得科学学位候选人的论文）在D。A.赖科夫和辩护的监督下，N。Ya. Vilenkin和S. V. Ptchelintsev.在这篇论文中，我把紧空间的Gelfand对偶推广到所有可分局部紧空间的范畴，把可分交换局部紧群的Pontryagin对偶推广到{ \em all}（可交换或非可交换）可分局部紧群的范畴。这些结果的获得分为几个阶段：1）拓扑对合代数的研究; 2）比紧空间更一般的空间的对偶的构造; 3）拓扑对合代数的张量积的研究; 4）实际获得所有分离的局部紧半群和群的对偶定理。
英文摘要：
The work is my Ph D thesis (dissertation for obtaining candidate of sciences degree in Russia) fulfilled under direction of D. A. Raikov and defended under supervision of N. Ya. Vilenkin and S. V. Ptchelintsev. In the dissertatin I gave generalizations of Gelfand duality for compact spaces to the category of all separated locally compact spaces, and of Pontryagin duality for separated commutative locally compact groups to the category of {\em all} (commutative or not) separated locally compact groups. Obtaining of these results has been divided into several stages: 1) the study of topological involutive algebras; 2) the construction of dualities for spaces more general than compact ones; 3) the study of tensor products of topological involutive algebras; 4) actually obtaining duality theorems for all separated locally compact semigroups and groups.
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