In this paper,we introduce the concepts of generalized regular points and narrow spectrumpoints of bounded linear operators on Hilbert spaces.The concept of generalized regular points is anextension of the concept regular points,and so,the set of all spectrum points is reduced to the narrowspectrum.We present not only the same and different properties of spectrum and of narrow spectrumbut also show the relationship between them.Finally,the well known problem about the invariantsubspaces of bounded linear operators on separable Hilbert spaces is simplified to the problem of theoperator with narrow spectrum only.
