On Certain Norm Inequalities for Inner Product Type Integral Transformers

Abstract

Studies on inner-product-type integral transformers have been considered in many research works from various perspectives, including spectra, numerical ranges, and operator inequalities. An open problem remains concerning inequalities related to norm estimates for inner-product-type integral transformers whose spectra are contained in the unit disc. It has been observed that the norms of such transformers can be attained under the condition that one of the implementing operators is normal. In this note, we address this problem by establishing norm inequalities for inner-product-type integral transformers in a general Banach space setting.