Tbilisi Mathematical Journal

Categorical construction of the ring of fractions

Mitali Routaray and A. Behera

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It is shown that the ring of fractions of the algebra of all bounded linear operators on a separable infinite dimensional Banach space is isomorphic to the Adams completion of the algebra with respect to a carefully chosen set of morphisms in the category of separable infinite dimensional Banach spaces and bounded linear norm preserving operators of norms at most 1.

Article information

Tbilisi Math. J., Volume 9, Issue 1 (2016), 1-8.

Received: 21 June 2015
Accepted: 15 December 2015
First available in Project Euclid: 12 June 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B07: Operators defined by compactness properties
Secondary: 55P60: Localization and completion

Category of fractions Calculus of left fractions Adams completion Grothedieck universe Ring of fractions


Routaray, Mitali; Behera, A. Categorical construction of the ring of fractions. Tbilisi Math. J. 9 (2016), no. 1, 1--8. doi:10.1515/tmj-2016-0001. https://projecteuclid.org/euclid.tbilisi/1528769037

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