## A Panorama of Modern Operator Theory and Related Topics: The Israel Gohberg Memorial VolumeHarry Dym, Marinus A. Kaashoek, Peter Lancaster, Heinz Langer, Leonid Lerer This book is dedicated to the memory of Israel Gohberg (1928–2009) – one of the great mathematicians of our time – who inspired innumerable fellow mathematicians and directed many students. The volume reflects the wide spectrum of Gohberg’s mathematical interests. It consists of more than 25 invited and peer-reviewed original research papers written by his former students, co-authors and friends. Included are contributions to single and multivariable operator theory, commutative and non-commutative Banach algebra theory, the theory of matrix polynomials and analytic vector-valued functions, several variable complex function theory, and the theory of structured matrices and operators. Also treated are canonical differential systems, interpolation, completion and extension problems, numerical linear algebra and mathematical systems theory. |

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### Contents

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Bregular Jinner Matrixvalued Functions | 50 |

Canonical Transferfunction Realization for SchurAglerclass Functions of the Polydisk | 75 |

Spectral Regularity of Banach Algebras and Noncommutative Gelfand Theory | 123 |

Banach Algebras of Commuting Toeplitz Operators on the Unit Ball via the Quasihyperbolic Group | 154 |

Canonical Models for Biisometries | 177 |

Firstorder Trace Formulae for the Iterates of the FoxLi Operator | 206 |

Bernstein Widths and Super Strictly Singular Inclusions | 358 |

On Inversion of Certain Structured Linear Transformations Related to Block Toeplitz Matrices | 377 |

The Inverse of a Twolevel Positive Definite Toeplitz Operator Matrix | 387 |

Parametrizing Structure Preserving Transformations of Matrix Polynomials | 403 |

A Review of Canonical Forms for Selfadjoint Matrix Polynomials | 425 |

Linearization Factorization and the Spectral Compression of a Selfadjoint Analytic Operator Function Under the Condition VM | 444 |

An Estimate for the Splitting of Holomorphic Cocycles One Variable | 465 |

The Discrete Algebraic Riccati Equation and Hermitian Block Toeplitz Matrices | 495 |

Factorization Versus Invertibility of Matrix Functions on Compact Abelian Groups | 225 |

Banded Matrices Banded Inverses and Polynomial Representations for Semiseparable Operators | 241 |

Description of HelsonSzegö Measures in Terms of the Schur Parameter Sequences of Associated Schur Functions | 269 |

Divide and Conquer Method for Eigenstructure of Quasiseparable Matrices Using Zeroes of Rational Matrix Functions | 298 |

An Identity Satisfied by Certain Orthogonal Vectorvalued Functions | 329 |

Invertibility of Certain Fredholm Operators | 345 |

On Cyclic and Nearly Cyclic Multiagent Interactions in the Plane | 513 |

A Trace Formula for Differential Operators of Arbitrary Order | 540 |

Jordan Structures and Lattices of Invariant Subspaces of Real Matrices | 571 |

Pseudospectral Functions for Canonical Differential Systems II | 583 |

Operator Identities for Subnormal Tuples of Operators | 613 |