According to the property of consistence in Fredholm index ,a new spectral set w as defined . By using the relationship betw een the spectral set and Brow der spectrum , the author gave the necessary and sufficient conditions for a bounded linear operator on a Hilbert space to satisfy the property (ω ) ,and characterized the property (ω ) of polyno mial functions .%根据一致Fredholm指标性质定义一种新的谱集,利用该谱集与Brow der谱之间的关系给出Hilbert 空间中有界线性算子满足(ω )性质的充要条件,并刻画多项式函数的(ω )性质 .
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