Abstract
The convex cone of positive semidefinite matrices of fixed size forms a commutative topological semigroup under the Hadamard product. In this paper we consider the closed subsemigroup of off-diagonal constant matrices, matrices having the same value in the off-diagonal positions, and its compact and convex subsemigroup of matrices with diagonal entries in the unit interval. Several results on these topological semigroups are presented: the group of units, (Löwner) ordered semigroup structures, one-parameter semigroups. An application of Hadamard powers obtained by FitzGerald and Horn and related open problems on Euclidean Jordan algebras are discussed.
| Original language | English |
|---|---|
| Pages (from-to) | 473-488 |
| Number of pages | 16 |
| Journal | Journal of Lie Theory |
| Volume | 30 |
| Issue number | 2 |
| State | Published - 2020 |
Keywords
- Euclidean Jordan algebra
- Hadamard semigroup
- infinitely divisible matrix
- Löwner order
- offdiagonal constant matrix
- one-parameter semigroup
- Positive semidefinite matrix
- Schur product theorem
- spin factor
- topological semigroup