Recent Advances in Operator Theory

On the spectral theory of degenerate quadratic operator pencils.- Two-sided tangential interpolation for Hilbert-Schmidt operator functions on polydisks.- Nonstationary analogs of the Herglotz representation theorem: realizations centered at an arbitrary point.- Characteristic functions of maximal sectorial operators.- Similarity between Krein space bicontractions and Hilbert space contractions.- Classification of cyclic invariant subspaces of Jordan operators.- Elliptic spectral problems of higher order with eigenparameter dependent boundary conditions.- About scattering on the ring.- Dilation of generalized Toeplitz kernels on lexicographic ? × R.- On Riccati equations and reproducing kernel spaces.- A status report on the asymptotic behavior of Toeplitz determinants with Fisher—Hartwig singularities.- On the spectrum of unbounded off-diagonal 2 × 2 operator matrices in Banach spaces.- Multithreshold spectral phase transitions for a class of Jacobi matrices.- Positive extensions and diagonally connected patterns.- Parametrized Furuta inequality and its applications.- J-symmetric factorizations and algebraic Riccati equations.- Scattering of waves by periodic gratings and factorization problems.- Corner of numerical ranges.- On some classes of extensions of sectorial operators and dual pairs of contractions.- Liftings of intertwining operators.- Some estimates for the resolvent and for the lengths of Jordan chains of an analytic operator function.- The Parrott problem for singular values.- Unconditional decompositions and Schur-type multipliers.- Scattering in a loop-shaped waveguide.- Pseudospectra of operator polynomials.