What's Happening

Matt Gibson ‘13

Matt Gibson profile

Student Research
Project Title: 
Metric-linear characterizations of operator algebra structures
Faculty Advisor(s): 
Matthew Neal, Associate Professor of Mathematics

Like most students, Matt Gibson had never heard of operator theory.

Undeterred, Matt learned how operators on Hilbert spaces model the observable properties of subatomic particles in quantum mechanics. He then dove right in and proved several new theorems! Matt gave several new “metric” characterizations of commuting operators, projections, invertible operators, and operator algebras in terms of matrix norms. In other words, he showed that “algebraic” conditions on operators are determined by conditions involving the “distance” between operators. In addition, he made a nontrivial contribution to a new characterization of C*-subalgebras up to complete isometry among subspaces of operator algebras. This result is contained in a paper of Dr. Neal's with David Blecher, Metric Characterizations II, which is to appear in the Illinois Journal of Mathematics in 2014. He is acknowledged there for his contribution. He then extended another result in that paper, giving a new proof that (in the finite dimensional case) the Shatten class of operators is not a unital operator space. In Neal and Blecher's paper this was only proved in dimension 2! Matt presented his work at joint AMS/MAA meetings this January, getting a warm reception. He is now pursuing a Ph. D. in Mathematics at the University of California at Irvine.

Posted Date: 
Monday, February 24, 2014
  • 11Matt Gibson profile