Abstract
Local operator spaces are defined to be projective limits of operator spaces. These limits arise when one considers linear spaces of unbounded operators, and they may be regarded as the “quantized” or “operator” analogues of locally convex spaces. It is shown that for nuclear spaces, the maximal and minimal quantizations coincide. Thus in a striking contrast to normed spaces, a nuclear space has precisely one quantization. Furthermore, it is shown that a local operator space is nuclear in the operator sense if and only if its underlying locally convex space is nuclear. Operator versions of bornology and duality are also considered.
Dedicated to the memory of Lajos Pukansky
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© 1997 Springer Science+Business Media Dordrecht
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Effros, E.G., Webster, C. (1997). Operator Analogues of Locally Convex Spaces. In: Katavolos, A. (eds) Operator Algebras and Applications. NATO ASI Series, vol 495. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5500-7_4
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DOI: https://doi.org/10.1007/978-94-011-5500-7_4
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