Annals of Functional Analysis

Scaled-free objects II

Will Grilliette

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Abstract

This work creates two categories of "array-weighted sets" for the purposes of constructing universal matrix-normed spaces and algebras. These universal objects have the analogous universal property to the free vector space, lifting maps completely bounded on a generation set to a completely bounded linear map of the matrix-normed space. Moreover, the universal matrix-normed algebra is used to prove the existence of a free product for matrix-normed algebras using algebraic methods.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 3 (2015), 216-261.

Dates
First available in Project Euclid: 17 April 2015

Permanent link to this document
https://projecteuclid.org/euclid.afa/1429286044

Digital Object Identifier
doi:10.15352/afa/06-3-18

Mathematical Reviews number (MathSciNet)
MR3336917

Zentralblatt MATH identifier
1341.46042

Subjects
Primary: 46M99: None of the above, but in this section
Secondary: 46B99: None of the above, but in this section 46H99: None of the above, but in this section

Keywords
Matrix-norm free construction left adjoint free product

Citation

Grilliette, Will. Scaled-free objects II. Ann. Funct. Anal. 6 (2015), no. 3, 216--261. doi:10.15352/afa/06-3-18. https://projecteuclid.org/euclid.afa/1429286044


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