Orthogonal vs. Non-Orthogonal Reducibility of Matrix-Valued Measures

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2016
• Hauptverfasser: Koelink, E., Román, P.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут математики НАН України 2016
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/147427
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.

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 elemen...