الفهرس 
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Abstract
In this thesis we study the spectrum and fine spectrum of some types of bounded linear operators, which are represented by certain infinite lower triangular matrices, as linear transformations on some sequence spaces. The thesis consists of two chapters:
Chapter 1: This chapter contains some concepts of spectral theory. Also, it contains some basic results which are needed for our investigation. The spectrum and fine spectrum of the operator on some sequence spaces are studied. It is proved, by counterexamples, that some recent results concerning the spectrum and fine spectrum of the operator over the sequence spaces and are incorrect. Also, the corresponding corrected results are provided. After that, the definition of the operator is modified by DROPping some condition and replacing other conditions by other suitable conditions. The spectrum and fine spectrum of the modified operator over some sequence spaces are determined. The results in this chapter improve several recent results.
Chapter 2: In this chapter, a new generalized difference operator is introduced. The class of the new operator includes all other operators studied before, which can be represented by lower triangular double-band matrices. The fine spectra of the operator on different sequence spaces are studied. Next, we show some ideas about changing the conditions in the fine spectrum of the operator . Also, we give some illustrative examples which show that the new results can be applied to different situations.