This book consists of invited survey articles and research papers in the scientific areas of the International Workshop on Operator Algebras, Operator Theory and Applications, which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems.

Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.

Indecomposable supercharacters of the infinite unitriangular group.- A nonlocal C*-algebra of singular integral operators with shifts and piecewise quasicontinuous coefficients.- Non-Hermitian quantum mechanics of bosonic operators.- Fredholm conditions on non-compact manifolds: theory and examples.- Statistical e-Convergence of Bögel-Type Continuous Functions.- Weighted statistical relative approximation by positive linear operators.- Descriptor systems under feedback and output injection.- Hermitian geometry on resolvent set (I).- Spectral algorithms for MRA orthonormal wavelets.- The NIEP.- Semi-Fredholmness of Weighted Singular Integral Operators with Shifts and Slowly Oscillating Data.- Factorization of singular integral operators with a Carleman backward shift: the vector case.- Extension-restriction theorems for algebras of approximation sequences.- Toeplitz and Hankel algebras - axiomatic and asymptotic aspects.- More than 40 years of algebraic techniquesin Numerical Analysis.- Linearizability of multi-control systems of the class C1 by additive change of controls.- The distance formula related to a family of projections orthogonal to their symmetries.