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Korean Mathematical Society (대한수학회)
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THE MINIMUM MODULUS OF A LINEAR MAP IN OPERATOR SPACES

  • Published : 2008.10.31
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Abstract

For a completely bounded linear maps between operator spaces, we introduce numbers which measure the degree of injectivity and subjectivity. The number measuring the injectivity is an operator space analogue of the minimum modulus of a linear map in normed spaces.

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References

  1. C. Apostol, The reduced minimum modulus, Michigan Math. J. 32 (1985), 279-294 https://doi.org/10.1307/mmj/1029003239
  2. D. P. Blecher and C. Le Merdy, Operator Algebras and Their Modules, London Math. Soc. Monograph, N. S. Vol. 30, Oxford Sc. Publ., 2004
  3. E. G. Effros and Z.-J. Ruan, Operator Spaces, London Math. Soc. Monograph, N. S. Vol. 23, Oxford Sc. Publ., 2000
  4. E. G. Effros and C. Webster, Operator analogues of locally convex spaces, Operator Algebras and Applications (Samos, 1996), pp. 163-207, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997
  5. H. A. Gindler and A. E. Taylor, The minimum modulus of a linear operator and its use in spectral theory, Studia Math. 22 (1962), 15-41 https://doi.org/10.4064/sm-22-1-15-41
  6. S. Goldberg, Unbounded Linear Operators: Theory and Applications, McGraw-Hill, 1966
  7. I. S. Hwang and W. Y. Lee, The reduced minimum modulus of operators, J. Math. Anal. Appl. 267 (2002), 679-694 https://doi.org/10.1006/jmaa.2001.7805
  8. T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, 1966
  9. S.-H. Kye and Z.-J. Ruan, On the local lifting property for operator spaces, J. Funct. Anal. 168 (1999), 355-379 https://doi.org/10.1006/jfan.1999.3475
  10. G. Pisier, Introduction to Operator Space Theory, London Math. Soc. Lecture. Note Ser. Vol. 294, Cambridge. Univ. Press, 2003
  11. Z.-J. Ruan, Subspaces of C*-algebras, J. Funct. Anal. 76 (1988), 217-230 https://doi.org/10.1016/0022-1236(88)90057-2