Quantization

自从量子力学出现以来，我们越来越经常地讨论非对易对象，但它们的内容范围很广。我们研究各种函数空间，这些空间上的一些算子，Hamilton算子和Dirac算子，算子之间的关系和不等式，算子代数，这些代数的自同构，自同构群，群的作用和余作用，首席研究员在C^<**>的内容中考虑了遍历理论中所谓的Rohlin性质的量子化问题。代数及其自同构由于我们必须使用范数拓扑，Rohlin性质的当前定义对代数和自同构施加了强限制（与冯诺依曼代数的情况相比），这可能表明进一步的推广是可取的。但只要我们坚持目前的定义，我们似乎已经得到了一般性的结果，进一步的结果如下：试图推广的结果，丰富的纯不变的状态，使经典和量子力学（岸本）之间的鲜明对比。各种功能空间，如哈代和伯格曼空间，如Toeplitz运营商和问题的不变子空间进行了调查（Nakazi）。研究了有界解析函数的点分离问题.分析了各种模型的哈密顿量、正则对易关系的表示和量子群的表示（荒井）。分类有限群的作用在冯诺依曼代数尝试（山之内）。

Ever since the advent of quantum mechanics we have treated non-commutative objects more and more often but their contents range wildly. We investigate various function spaces, some operators on these spaces, Hamiltonians and Dirac operators, relations and inequalities among operators, algebras of operators, automorphisms of these algebras, groups of automorphisms, actions and coactions of groups, representations of quantum groups etc. The head investigator considered the problem of quantizing the so-called Rohlin property in ergodic theory in the contents of C^<**>-algebras and their automorphisms. Since we must use norm topology, the present definition of the Rohlin property imposes strong restrictions on the algebras and automorphisms (compared with the von Neumann algebra case), which may suggest a further generalization is desirable. But as far as we stick to the present definition, we seem to have reached general results.Further results are as follows : A generalization is attempted for a result of abundance of pure in-variant states which makes a sharp contrast between classical and quantum mechanics (Kishimoto). Various function spaces such as Hardy and Bergman spaces, such operators as Toeplitz operators and the problem of invariant subspaces are investigated (Nakazi). The problem of separation of points are studied for bounded analytic functions (Hayashi). Hamiltonians of various models, repre-sentations of canonical commutation relations, and representations of quantum groups are analized (Arai). Classification of coactions of finite groups on von Neumann algebras are attempted (Yamanouchi).