Operator theory functional analysis and applications This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications” held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras Sturm Liouville theory integrable systems dilation theory frame theory Toeplitz Hankel and singular integral operators to questions from lattice group and matrix theories complex analysis harmonic analysis and function spaces. Given its scope the book is chiefly intended for researchers and graduate students in the areas of Operator Theory Functional Analysis their applications and adjacent fields.