@article {28064, title = {Synthetic properties of locally compact groups: preservation and transference}, journal = { Monatshefte f{\"u}r Mathematik}, volume = {201}, year = {2023}, pages = {329-347}, abstract = {Using techniques from TRO equivalence of masa bimodules we prove various transference results: We show that when α is a group homomorphism which pushes forward the Haar measure of G to a measure absolutely continuous with respect to the Haar measure on H, then (α{\texttimes}α)-1 preserves sets of compact operator synthesis, and conversely when α is onto. We also prove similar preservation results for operator Ditkin sets and operator M-sets, obtaining preservation results for M-sets as corollaries. Some of these results extend or complement existing results of Ludwig, Shulman, Todorov and Turowska.}, url = {https://doi.org/10.1007/s00605-022-01736-8}, author = {M. Anoussis, G. K. Eleftherakis, A. Katavolos} }