On rings of operators. II
On rings of operators. II
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DOI：
10.1090/s0002-9947-1937-1501899-4
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发表时间：
1937-02
影响因子：
1.3
通讯作者：
F. Murray;J. Neumann
中科院分区：
文献类型：
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作者：
F. Murray;J. Neumann
导论.本文是同一作者的一篇论文的继续：On rings of operators，Annals of Mathematics，（2），vol. 37（1936），pp. 116-229.它包含了某些遗留问题的解决方案。我们将证明迹TrMiA）的一般可加性，它的弱连续性，以及§，M和M'之间的某些同构（参见。（见上述文件结尾处的备注（i）至（iv））。所有这些考虑都指的是M的“情况（II）”（cf. Theorem VIII，loc. cit.）。通过得到一个表示m（TrMiA）=（iAgi，gi）t-i，建立了Tr（A）的性质
Introduction. This paper is a continuation of one by the same authors : On rings of operators, Annals of Mathematics, (2), vol. 37 (1936), pp. 116-229. It contains the solution of certain problems which were left open there. We will prove the general additivity of trace TrMiA), its weak continuity, and certain isomorphisms between §, M, and M' (cf. the remarks (i)-(iv) at the end of the above quoted paper). All these considerations refer to "Case (II)" for M (cf. Theorem VIII, loc. cit.). The properties of Tr¡niA) are established by obtaining for it a representation m TrMiA) = £ iAgi, gi) t-i