Abstract
We show that the interpolation curve joining any two homogeneous Hilbertian operator spaces of the same dimension is a geodesic in the metric space defined by the completely bounded Banach-Mazur distance. In proving this result we obtain explicit formula for the distance between certain well known operator spaces.
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References
Effros, E.G., Ruan, Z.-G.: Operator Spaces. Oxford Science Publications, Oxford (2000)
Bridson, M., Haelfinger, A.: Metric Spaces of Non-Positive Curvature. Springer, Berlin (1999)
Mathes, B.: A completely bounded view of Hilbert-Schmidt operators. Houst. Math. J. 17, 404–418 (1991)
Mathes, B.: Characterizations of row and column Hilbert spaces. J. Lond. Math. Soc. 50(2), 199–208 (1994)
Pisier, G.: The operator space OH, complex interpolation and tensor norms. Mem. AMS 122(585) (1996)
Pisier, G.: Introduction to Operator Space Theory. London Mathematical Society Lecture Note Series, vol. 294. Cambridge University Press, London (2003)
Junge, M., Pisier, G.: Bilinear forms on exact operator spaces and \(B(H)\otimes B(H)\). Geom. Funct. Anal. 5(2), 329–363 (1995)
Dineen, S., Radu, C.: Distances Between Hilbertian Operator Spaces (submitted)
Zhang, C.: Completely bounded Banach-Mazur distance. Proc. Edinb. Math. Soc. 40(2), 247–260 (1997)
Acknowledgments
The author is expressing her gratitude for Professor Seán Dineen’s helpful suggestions and comments. The work was carried out with the support of Programa de Apoio ao Pós-Doutorado no Estado do Rio de Janeiro, Parceria CAPES/FAPERJ, Edital FAPERJ 10/2011, Brazil.
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Radu, C. Geodesics between Hilbertian operator spaces. RACSAM 108, 917–922 (2014). https://doi.org/10.1007/s13398-013-0151-5
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DOI: https://doi.org/10.1007/s13398-013-0151-5