Taiwanese Journal of Mathematics

Quotients of Quantum Bornological Spaces

Anar Dosi

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In the note we investigate the main duality properties of quantum (or local operator) spaces involving quantum bornology. Namely, we prove that each finite complete bornology admits precisely one quantization and each complete quantum space is a matrix bornology quotient of a local trace class algebra.

Article information

Taiwanese J. Math., Volume 15, Number 3 (2011), 1287-1303.

First available in Project Euclid: 18 July 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47L25: Operator spaces (= matricially normed spaces) [See also 46L07]
Secondary: 46L07: Operator spaces and completely bounded maps [See also 47L25]

quantum bornological spaces absolutely matrix convex set matrix seminorm Hilbert-Schmidt boundary exact matrix quotient mapping


Dosi, Anar. Quotients of Quantum Bornological Spaces. Taiwanese J. Math. 15 (2011), no. 3, 1287--1303. doi:10.11650/twjm/1500406300. https://projecteuclid.org/euclid.twjm/1500406300

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  • D. P. Blecher, The standard dual of an operator space, Pacific J. Math., 153(1) (1992), 15-30.
  • D. P. Blecher and V. I. Paulsen, Tensor products of quantum normed spaces, J. Funct. Anal., 99 (1991), 262-292.
  • D. P. Blecher, Notes on duality methods and operator spaces, http://www.math.uh.edu/ \symbol126dblecher/op.pdf
  • A. A. Dosiev, Local operator spaces, unbounded operators and multinormed $C^{\ast}$-algebras, J. Funct. Anal., 255 (2008), 1724-1760.
  • A. A. Dosi, Local operator algebras, fractional positivity and quantum moment problem, Trans. AMS, 363 (2011), 801-856.
  • A. A. Dosi, Noncommutative Mackey theorem, Intern. J. Math., 22(3) (2011), 1-7.
  • A. A. Dosi, Quantum domains, inductive limits and matrix duality, J. Math. Physics, 51(6) (2010), 1-43.
  • R. E. Edwards, Functional Analysis, Theory and Apllications, Holt, Rinehart and Winston, 1965.
  • E. G. Effros and Z.-J. Ruan, Operator spaces, London Math. Soc., Clarendon Press-Oxford, 2000.
  • E. G. Effros and C. Webster, Operator analogues of locally convex spaces, Operator Algebras and Applications, (Samos 1996), (Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495), Kluwer, 1997.
  • A. Ya. Helemskii, Quantum functional analysis: Non-Coordinate Approach, AMS, Univ. Lect. Ser., 2010.
  • H. Hogbe-Nlend, Bornologies and functional analysis: introductory course on the theory of duality topology-bornology and its use in functional analysis, Elsevier, 1977.
  • R. Meyer, Analytic cyclic cohomology, PhD. Universität Münster, 1999.
  • H. Schaefer, Topological vector spaces, Springer-Verlag, 1970.
  • C. Webster, Local operator spaces and applications, Ph.D. University of California, Los Angeles, 1997.