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Journal article
Convex Entire Noncommutative Functions are Polynomials of Degree Two or Less
Integral equations and operator theory, v 86(2), pp 151-163
01 Oct 2016
Abstract
This paper concerns matrix "convex" functions of (free) noncommuting variables, . It was shown in Helton and McCullough (SIAM J Matrix Anal Appl 25(4):1124-1139, 2004) that a polynomial in which is matrix convex is of degree two or less. We prove a more general result: that a function of that is matrix convex near and also that is "analytic" in some neighborhood of the set of all self-adjoint matrix tuples is in fact a polynomial of degree two or less. More generally, we prove that a function in two classes of noncommuting variables, and that is both"analytic" and matrix convex in on a "noncommutative open set" in is a polynomial of degree two or less.
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Details
- Title
- Convex Entire Noncommutative Functions are Polynomials of Degree Two or Less
- Creators
- J. William Helton - University of California, San DiegoJ. E. Pascoe - University of California, San DiegoRyan Tully-Doyle - Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USAVictor Vinnikov - Ben-Gurion University of the Negev
- Publication Details
- Integral equations and operator theory, v 86(2), pp 151-163
- Publisher
- Springer Nature
- Number of pages
- 13
- Grant note
- DMS-1201498; DMS-1361720 / NSF; National Science Foundation (NSF) 322/00 / Israel Science Foundation Ford Motor Co.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000387436500001
- Scopus ID
- 2-s2.0-84990866012
- Other Identifier
- 991021879781204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics