Applications of Alughte Transform for Berezin Radius Inequalities

Abstract

– In functional analysis, linear operators induced by functions are frequently encountered; these contain Hankel operators, constitution operators, and Toeplitz operators. The symbol of the resultant operator is another name for the inciting function. In many instances, a linear operator on a Hilbert space ℋ results in a function on a subset of a topological space. As a result, we regularly investigate operators induced by functions, and we may also investigate functions induced by operators. The Berezin sign is a wonderful representation of an operator-function relationship. F. Berezin proposed the Berezin switch in [8], and it has proven to be a vital tool in operator theory given that it utilizes many essential aspects of significant operators. Many mathematicians and physicists are fascinated by the Berezin symbol of an operator defined on the functional Hilbert space. The Berezin radius inequality has been extensively studied in this situation by a number of mathematicians. In this paper, we use the Alughte transform and the generalized Alughte transform to develop Berezin radius inequalities for Hilbert space operators. We additionally offer fresh Berezin radius inequality results. Huban et al. [15] and Başaran et al. [6] supply the Berezin radius inequality.