Reproducing kernels and Aluthge transforms

We will discuss the merge of three operator and function theoretic concepts, namely, reproducing kernels, Aluthge transforms, and left invertible operators. Our primary interest will be on the computational part of the Aluthge transform of shifts on (concrete) analytic reproducing kernel Hilbert spaces. Along the way, we will also examine and compare different tools/techniques (like Shimorin models of left invertible operators) and point out the subtlety of the theory of Aluthge transform. This talk is about joint work with Susmita Das.