Unitary extensions of isometries, generalized interpolation and band extensions

Rodrigo Arocena

Banach Center Publications (1997)

  • Volume: 38, Issue: 1, page 17-23
  • ISSN: 0137-6934

Abstract

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The aim of this paper is to give a very brief account of some applications of the method of unitary extensions of isometries to interpolation and extension problems.

How to cite

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Arocena, Rodrigo. "Unitary extensions of isometries, generalized interpolation and band extensions." Banach Center Publications 38.1 (1997): 17-23. <http://eudml.org/doc/208625>.

@article{Arocena1997,
abstract = {The aim of this paper is to give a very brief account of some applications of the method of unitary extensions of isometries to interpolation and extension problems.},
author = {Arocena, Rodrigo},
journal = {Banach Center Publications},
keywords = {extensions of isometries; interpolation and extension problems},
language = {eng},
number = {1},
pages = {17-23},
title = {Unitary extensions of isometries, generalized interpolation and band extensions},
url = {http://eudml.org/doc/208625},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Arocena, Rodrigo
TI - Unitary extensions of isometries, generalized interpolation and band extensions
JO - Banach Center Publications
PY - 1997
VL - 38
IS - 1
SP - 17
EP - 23
AB - The aim of this paper is to give a very brief account of some applications of the method of unitary extensions of isometries to interpolation and extension problems.
LA - eng
KW - extensions of isometries; interpolation and extension problems
UR - http://eudml.org/doc/208625
ER -

References

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  2. [A.1] R. Arocena, Schur analysis of a class of translation invariant forms, in: Analysis and Partial Differential Equations: A Collection of Papers dedicated to Mischa Cotlar, C. Sadosky (ed.), Marcel Dekker, New York and Basel, 1990. Zbl0703.47021
  3. [A.2] R. Arocena, Some remarks on lifting and interpolation problems, Rev. Un. Mat. Argentina 37 (1991), 200-211. 
  4. [A.3] R. Arocena, Unitary colligations and parametrization formulas, Ukrainian Math. J. 46 (1994), 147-154. 
  5. [A.4] R. Arocena, On the Nagy-Foiaş-Parrott commutant lifting theorem, in: Contemp. Math. 189, Amer. Math. Soc., 1995, 55-64. Zbl0837.47006
  6. [A.5] R. Arocena, Unitary extensions of isometries and interpolation problems: (1) dilation and lifting theorems, Publ. Mat. Uruguay 6 (1995), 137-158. 
  7. [AG] D. Z. Arov and L. Z. Grossman, Scattering matrices in the theory of unitary extensions of isometric operators, Soviet Math. Dokl. 27 (1983), 518-522. Zbl0543.47010
  8. [DG.1] H. Dym and I. Gohberg, Extensions of kernels of Fredholm operators, J. Analyse Math. 42 (1982/83), 51-97. 
  9. [DG.2] H. Dym and I. Gohberg, A new class of contractive interpolants and maximun entropy principles, in: Oper. Theory Adv. Appl. 29, Birkhäuser, 1988, 117-150. 
  10. [FF] C. Foiaş and A. E. Frazho, The Commutant Lifting Approach to Interpolation Problems, Birkhäuser, Basel, 1990. Zbl0718.47010
  11. [FFG] C. Foiaş, A. E. Frazho and I. Gohberg, Central intertwining lifting, maximum entropy and their permanence, Integral Equations Operator Theory 18 (1994), 166-201. Zbl0812.47013
  12. [GKW.1] I. Gohberg, M. A. Kaashoek and H. J. Woerdeman, The band method for positive and contractive extension problems, J. Operator Theory 22 (1989), 109-115. Zbl0697.46022
  13. [GKW.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 (1989), 343-382. Zbl0676.46043
  14. [GKW.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 (1991), 231-254. Zbl0728.47013
  15. [N] N. K. Nikol'skiĭ, Treatise on the Shift Operator, Springer, New York, 1986. 
  16. [P] S. Parrott, On a quotient norm and the Sz.-Nagy-Foiaş lifting theorem, J. Funct. Anal. 30 (1978), 311-328. Zbl0409.47004
  17. [S] D. Sarason, Generalized interpolation in H , Trans. Amer. Math. Soc. 127 (1967), 179-203. Zbl0145.39303
  18. [Sz.-NF] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970. Zbl0201.45003

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