The present volume is the first of two volumes containing a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The focus in this volume is on operator theory, linear algebra, and analytic functions. Further, a commemorative article of speeches and reminiscences dedicated to Israel Gohberg is presented.

Zusammenfassung
This is the first volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Inhalt
A Quantitative Estimate for Bounded Point Evaluations in Pt(?)-spaces.- WEighted Composition Operators on the Bloch Space of a Bounded Homogeneous Domain.- Images of Minimal-Vector Sequences Under Weighted Composition Operators on L2( ).- On Extensions of Indefinite Toeplitz-Kre?n-Cotlar triplets.- Multivariable Weighted Composition Operators: Lack of Point Spectrum, and Cyclic Vectors.- Factorization Algorithm for Some Special Non-rational Matrix Functions.- Structured Primal-dual Interior-point Methods for Banded Semidefinite Programming.- A Note on Semi-Fredholm Hilbert Modules.- The S-recurrence of Schur Parameters of Non-inner Rational Schur Functions.- Curvature of Universal Bundles of Banach Algebras.- A Contractive Operator View on an Inversion Formula of Gohberg-Heinig.- A Spectral Weight Matrix for a Discrete Version of Walsh's Spider.- Norm Inequalities for Composition Operators on Hardy and Weighted Bergman Spaces.- Theory vs. Experiment: Multiplicative Inequalities for the Numerical Radius of Commuting Matrices.- Best Constant Inequalities Involving the Analytic and Co-Analytic Projection.- Quasi Commutativity of Regular Matrix Polynomials: Resultant and Bezoutian.- Quasidiagonal Extensions of the Reduced Group C*-algebras of Certain Discrete Groups.- Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves.- Almost Periodic Polynomial Factorization of Some Triangular Matrix Functions.- Revisit to a Theorem of Wogen.- Survey on the Best Constants in the Theory of One-dimensional Singular Integral Operators.- Gantmacher-Krein Theorem for 2-totally Nonnegative Operators in Ideal Spaces.- Conditions for Linear Dependence of Two Operators.- Matrix Inequalities and Twisted Inner Products.- The Spectrum of a CompositionOperator and Calderón's Complex Interpolation.- Almost Periodic Factorization of 2 × 2 Triangular Matrix Functions: New Cases of Off Diagonal Spectrum.- Infinite Hankel Block Matrices, Extremal Problems.- On Compactness of Operators in Variable Exponent Lebesgue Spaces.- Extension to an Invertible Matrix in Convolution Algebras of Measures Supported in [0,+?).- The Invariant Subspace Problem via Composition Operators-redux.- On Norms of Completely Positive Maps.- Some Exponential Inequalities for Semisimple Lie Groups.- Parabolic Quasi-radial Quasi-homogeneous Symbols and Commutative Algebras of Toeplitz Operators.- Algebraic Aspects of the Paving and Feichtinger Conjectures.- Dominating the Commutator.