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The Band Method for Bordered Algebras

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Contributions to Operator Theory and its Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 62))

Abstract

The band method for positive definite extension problems of non-band type is specified for the bordered case. A fractional type description of all positive extensions is new. We illustrate the result for Fredholm integral operators. The notion of Schur complement plays a crucial role.

Partially supported by NASA contract NAS1-18347

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References

  1. I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, The Band Method For Positive and Contractive Extension Problems. J. Operator Theory 22: 109–155, 1989.

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  2. I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, The Band Method For Positive and Contractive Extension Problems: an Alternative Version and New Applications. Integral Equations Operator Theory 12: 343–382, 1989.

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  3. I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, A Maximum Entropy Principle in the General Framework of the Band Method. J. Funct. Anal. 95: 231–254, 1991.

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  4. I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, The Band Method for Positive Extension Problems of Non-Band Type, J. Operator theory, to appear.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Tel Aviv University, Ramat Aviv, 69978, Israel

    I. Gohberg

  2. Department of Mathematics, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek

  3. Department of Mathematics, College of William and Mary, Williamsburg, Virginia, 23187-8795, USA

    H. J. Woerdeman

Authors
  1. I. Gohberg
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  2. M. A. Kaashoek
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  3. H. J. Woerdeman
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Editor information

T. Furuta I. Gohberg T. Nakazi

Additional information

Dedicated to Professor T. Ando, on the occasion of his sixtieth birthday

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© 1993 Springer Basel AG

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Gohberg, I., Kaashoek, M.A., Woerdeman, H.J. (1993). The Band Method for Bordered Algebras. In: Furuta, T., Gohberg, I., Nakazi, T. (eds) Contributions to Operator Theory and its Applications. Operator Theory: Advances and Applications, vol 62. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8581-2_5

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  • DOI: https://doi.org/10.1007/978-3-0348-8581-2_5

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9690-0

  • Online ISBN: 978-3-0348-8581-2

  • eBook Packages: Springer Book Archive

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