As we all know, sequence space theory has become an independent branch of functional analysis. The research on sequence space can be traced back to D. Hilbert's research on square sum sequence space l2, and then there are researches on P-degree sum sequence space lp( 1≤), bounded sequence space L, convergent sequence space C and so on. These sequence spaces are very specific. All belong to the category of normed space. 1934 0.Toeplitz and C. Kothe introduced and discussed the perfect sequence space for the first time in their influential papers. It is a general sequence space, including most but not all specific sequence spaces studied before, such as LP (1 ≤ p).

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