| 摘 要： | The spectral theory of selfadjoint operators and unitary operators in Hilbert spacehas been successfully generalized to Π_k space.However,there are only a few results for thespectral theory of selfadjoint operators and unitary operators in Π space.One of theimportant reasons is that the structure of Π space is more complex than that of Π_k space.This paper and the forthcoming paper “The structure of Π space(Ⅱ)”will mainly be dealtwith the structure of Ⅱ spaces,which will be used to further study the operators in Ⅱspaces.
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