Geodesic
HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM – II
Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 376-396

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We continue our investigation of the real space H of Hermitian matrices in $${M_n}(\mathbb{C})$$ with respect to norms on $${\mathbb{C}^n}$$. We complete the commutative case by showing that any proper real subspace of the real diagonal matrices on $${\mathbb{C}^n}$$ can appear as H. For the non-commutative case, we give a complete solution when n=3 and we provide various illustrative examples for n ≥ 4. We end with a short list of problems. 
DUNCAN, JOHN; McGREGOR, COLIN M. HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM – II. Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 376-396. doi: 10.1017/S0017089521000173
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     author = {DUNCAN, JOHN and McGREGOR, COLIN M.},
     title = {HERMITIANS {IN} {MATRIX} {ALGEBRAS} {WITH} {OPERATOR} {NORM} {\textendash} {II}},
     journal = {Glasgow mathematical journal},
     pages = {376--396},
     year = {2022},
     volume = {64},
     number = {2},
     doi = {10.1017/S0017089521000173},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089521000173/}
}
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