Recent Advances in Operator Theory and Related Topics

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This work explores various advanced topics in operator theory and functional analysis. It covers inverse problems related to canonical differential systems and the construction of Schwarz norms. The text delves into extremal extensions of nonnegative operators and discusses Livšic—Brodskii nodes with strongly regular J-inner characteristic matrix functions within the Hardy class. It examines scalar perturbations of the Sz. Nagy—Foias characteristic function and presents inequalities for eigenvalues of sums in von Neumann algebras. The book also addresses weighted variants of the Three Chains Completion Theorem and semigroups in finite von Neumann algebras. Additional topics include singly generated algebras with compact operators, analytic extensions of vector-valued functions, and the structure of spherical contractions. It highlights hyper-reflexivity in Apostol’s bilateral weighted shifts and explores Wielandt-type extensions of the Heinz—Kato—Furuta inequality. The generalized von Neumann inequality, ultraproducts of C*-algebras, and intertwining extensions are also discussed. The work investigates self-polar Hilbertian norms, Schur norms, and the multivariate von Neumann inequality. It analyzes spectral properties of self-adjoint Jacobi matrices, the hyperinvariant subspace problem, and stability in average on a Markov background. The text concludes with discussions on spectral singularities, invariant measures for sto