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N^p-SPACES
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초록
We introduce a new norm, called the N^p-norm (1 ≤ p < ∞)on the space N^p(V,W) where V and W are abstract operator spaces. By proving some fundamental properties of the space N^p(V,W), we also discover that if W is complete, then the space N^p(V,W) is also a Banach space with respect to this norm for 1 ≤ p < ∞.
Abstract
We introduce a new norm, called the N^p-norm (1 ≤ p < ∞)on the space N^p(V,W) where V and W are abstract operator spaces. By proving some fundamental properties of the space N^p(V,W), we also discover that if W is complete, then the space N^p(V,W) is also a Banach space with respect to this norm for 1 ≤ p < ∞.
참고문헌 (9)
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- V. Paulsen, "Representations of function algebras, abstract operator spaces, and Banach space geometry", J. Funct. Anal, 109(1), pp.113~129 (1992)
- G. Pisier, "Introduction to Operator Space Theory" (2003), Cambridge University Press
- R. Smith, "Completely bounded maps between C*-algebras", J. London Math. Soc, 27(1), pp.157~166 (1983)
- W. Stinespring, "Positive functions on C*-algebras", Proc. Amer. Math. Soc, 6, pp.211~216 (1955)
- G. Wittstock, "Ein operatorwertiger Hahn-Banach Satz", J. Funct. Anal, 40(2), pp.127~150 (1981)
- G. Wittstock, "Extensions of completely bounded module morphisms", Proc. Conference on Op- erator Algebras and Group Representations (1983), Neptum, Pitman
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