The winners of the Best Paper award: published in the years 2023 and 2024 in Advance in Operator Theory (AIOT): co-authors, Jorgensen, Palle E. T.; Tian, James. Title: Hilbert space valued Gaussian processes, their kernels, factorizations, and covariance structure. Adv. Oper. Theory 9 (2024), no. 4, Paper No. 77, 17 pp.