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Matricial Coupling and Equivalence After Extension

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Operator Theory and Complex Analysis

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 59))

Abstract

The purpose of this paper is to clarify the notions of matricial coupling and equivalence after extension. Matricial coupling and equivalence after extension are relationships that may or may not exist between bounded linear operators. It is known that matricial coupling implies equivalence after extension. The starting point here is the observation that the converse is also true: Matricial coupling and equivalence after extension amount to the same. For special cases (such as, for instance, Fredholm operators) necessary and sufficient conditions for matricial coupling are given in terms of null spaces and ranges. For matrices, the issue of matricial coupling is considered as a completion problem.

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Authors and Affiliations

  1. Econometric Institute Rotterdam, Erasmus University, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    H. Bart

  2. 18 Capen Blvd, Buffalo, N.Y., 14214, USA

    V. E. Tsekanovskii

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  1. H. Bart
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  2. V. E. Tsekanovskii
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Editors and Affiliations

  1. Research Institute for Electronic Science, Hokkaido University, Sapporo, 060, Japan

    T. Ando

  2. Raymond and Beverly Sackler Faculty of Exact Sciences School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

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© 1992 Springer Basel AG

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Bart, H., Tsekanovskii, V.E. (1992). Matricial Coupling and Equivalence After Extension. In: Ando, T., Gohberg, I. (eds) Operator Theory and Complex Analysis. Operator Theory: Advances and Applications, vol 59. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8606-2_6

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  • DOI: https://doi.org/10.1007/978-3-0348-8606-2_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9699-3

  • Online ISBN: 978-3-0348-8606-2

  • eBook Packages: Springer Book Archive

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