A BOUNDED OPERATOR APPROACH TO TOMITA-TAKESAKI THEORY
A BOUNDED OPERATOR APPROACH TO TOMITA-TAKESAKI THEORY
复制标题
富田竹崎理论的有界算子方法
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
A. V. Daele
中科院分区：
文献类型：
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作者：
M. Rieffel;A. V. Daele
我们证明了算子Δu和J实际上可以与复Hubert空间的任何相当一般的真实的子空间相联系，并且它们的许多性质，例如Au的K.M.S.条件，可以在这个不太复杂的设置中导出。在后半部分的文件，我们表明，通过使用一些想法，从上半年，简化证明富田竹崎理论最近由第二作者可以重新完全在有界算子，从而进一步简化它，除其他事项外，消除所有考虑涉及域的无界算子。
of the paper we show that the operators Δu and J can, in fact, be associated with any fairly general real subspace of a complex Hubert space, and that many of their properties, for example the characterization of Au in terms of the K.M.S. condition, can be derived in this less complicated setting. In the second half of the paper we show, by using some of the ideas from the first half, that a simplified proof of the Tomita-Takesaki theory given recently by the second author can be reformulated entirely in terms of bounded operators, thus further simplifying it by, among other things, eliminating all considerations involving domains of unbounded operators.