Honors Thesis: "“On Schur-Agler Class Preserving Multipliers"

Abstract: Our investigation begins with Schur multipliers, the operators preserving Schur class, which arise in the study of bounded linear operators on Hilbert spaces. Subsequently, we turn our focus to Agler multipliers, which are closely related to commutative contractions. Throughout our study, we emphasize the interplay between Schur and Agler multipliers, shedding light on the similarities and differences between these two classes. We revisit Small's seminal work on convolution techniques and their applications in functional analysis. Inspired by Small's innovative approach, we bridge the gap between Schur multipliers and Agler multipliers. Examples, including Fejér means multipliers, as well as a conjecture about the general form concerning the characterization of Agler multipliers are introduced.