In this paper, the study extended eigenvalues and extended eigenvectors, and we will investigate the  and give for some concepts properties and result important, also we will find the  and  on the  space, so U is Unilateral shift operator and .   http://dx.doi.org/10.25130/tjps.24.2019.119

The study focused on expanding the concept of 2-normed spaces by developing a new definition ( -normed space), and the study concentrated on the convergent of sequences and Cauchy sequences in our definition, as well as some other branches such as linear transformation and contraction.   http://dx.doi.org/10.25130/tjps.24.2019.078

The study focuses on α–almost similar operator which is a new concept of the operator theory and also some basic concepts related to the concept α–almost similar. The study also defines a new concept called   which is an expansion of the concept  and the relationship of this concept with the α–almost similar. At the end of this research, we study some important relationships among similar, unitarily equivalent, and almost similar on the one hand and α–almost similar on the other.   http://dx.doi.org/10.25130/tjps.24.2019.094

In this paper, the study extended eigenvalues and extended eigenvectors, and we will investigate the  and give for some concepts properties and result important, also we will find the  and  on the  space, so U is Unilateral shift operator and .

No abstract