Tbilisi Mathematical Journal

Categorical construction of the ring of fractions

Mitali Routaray and A. Behera

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769037

Digital Object Identifier
doi:10.1515/tmj-2016-0001

Mathematical Reviews number (MathSciNet)
MR3456779

Zentralblatt MATH identifier
1382.46058

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

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

Citation

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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References

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