eng Science and Education Publishing Turkish Journal of Analysis and Number Theory 2333-1232 2022-12-30 10 1 21 26 10.12691/tjant-10-1-5 TJANT20221015 article Zameddin I. Ismailov zameddin.ismailov@gmail.com 1 Pembe Ipek Al 1 Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey In the present study, firstly, some algebraic inequalities are proved, which will be used later. By making use of these relations, some evaluations are found related the gaps between norm and numerical radius, spectral radius and Crawford number for diagonal block operator matrices on the infinite direct sum of Hilbert spaces. Later on, the gaps between some spectral characteristic numbers (operator norm, lower and upper bounds of spectrum set and numerical radius) of the infinite direct sum of Hilbert space operators relatively to the same spectral characteristics of the coordinate operators are investigated. Then, the obtained results are supported by applications. The open problem posed by Demuth in 2015 and the works of Kittaneh and his researcher group in this area had an important effect on the formation of the subject discussed in this study. http://pubs.sciepub.com/tjant/10/1/5/tjant-10-1-5.pdf operator norm spectral radius numerical radius CRAWFORD number