The spectral radius of bounded linear operators and related inequalities

This thesis consists of two chapters. In the first chapter, a general literature review about the spectral radius of bounded linear operators is made. In addition, fundamental informations related to the terms are used in this thesis were given with descriptive examples. The second chapter consists of five sections. In the first section, a theorem on the spectral radius of sums of bounded linear operators defined in Banach spaces is mentioned. In the second part, the spectral radius inequalities for the sums, products and commutators of Hilbert space operators are given. In the third section, the conditions implying the semi-nilpotentiality of the commutators of two positive commutative operators defined in Banach spaces are mentioned. In the fourth section, inequalities related to local spectral radius of sums and products of bounded linear operators defined in Banach spaces are given. In the last part, some sufficient conditions are given for the sub-additivity and sub-multiplicability of the local spectral radii of the bounded linear operators defined in Banach spaces. Keyword: Spectral radius, local spectral radius, commutator, positive operator, operator matrix, inequality