Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures
|
|
| Creator |
Koelink, E.
Román, P. |
|
| Description |
A matrix-valued measure Θ reduces to measures of smaller size if there exists a constant invertible matrix M such that MΘM∗ is block diagonal. Equivalently, the real vector space A of all matrices T such that TΘ(X)=Θ(X)T∗ for any Borel set X is non-trivial. If the subspace Ah of self-adjoints elements in the commutant algebra A of Θ is non-trivial, then Θ is reducible via a unitary matrix. In this paper we prove that A is ∗-invariant if and only if Ah=A, i.e., every reduction of Θ can be performed via a unitary matrix. The motivation for this paper comes from families of matrix-valued polynomials related to the group SU(2)×SU(2) and its quantum analogue. In both cases the commutant algebra A=Ah⊕iAh is of dimension two and the matrix-valued measures reduce unitarily into a 2×2 block diagonal matrix. Here we show that there is no further non-unitary reduction.
|
|
| Date |
2019-02-14T18:23:07Z
2019-02-14T18:23:07Z 2016 |
|
| Type |
Article
|
|
| Identifier |
Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures / E. Koelink, P. Román // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 12 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33D45; 42C05 DOI:10.3842/SIGMA.2016.008 http://dspace.nbuv.gov.ua/handle/123456789/147427 |
|
| Language |
en
|
|
| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
|
|
| Publisher |
Інститут математики НАН України
|
|