2014
DOI: 10.15352/afa/1396833505
|View full text |Cite
|
Sign up to set email alerts
|

Orthogonally additive and orthogonally multiplicative holomorphic functions of matrices

Abstract: Abstract. Let H : M m → M m be a holomorphic function of the algebra M m of complex m × m matrices. Suppose that H is orthogonally additive and orthogonally multiplicative on self-adjoint elements. We show that either the range of H consists of zero trace elements, or there is a scalar sequence {λ n } and an invertible S in M m such thatHere, x t is the transpose of the matrix x. In the latter case, we always have the first representation form when H also preserves zero products. We also discuss the cases wher… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
4
0

Year Published

2016
2016
2018
2018

Publication Types

Select...
4

Relationship

1
3

Authors

Journals

citations
Cited by 4 publications
(4 citation statements)
references
References 17 publications
0
4
0
Order By: Relevance
“…For holomorphic maps of matrices, we have a counterpart to Theorem 3.3. The following examples borrowed from [14,9] tell us that one cannot get a complete analog to Theorem 3.3 for the non-commutative case. We also remark that Example 3.9(c) below tells us that a similar conclusion of [21, Theorem 18] for orthogonally additive and doubly orthogonality preserving holomorphic functions does not hold for zero product preserving ones.…”
Section: Orthogonally Additive and Zero Product Preserving Holomorphimentioning
confidence: 99%
See 3 more Smart Citations
“…For holomorphic maps of matrices, we have a counterpart to Theorem 3.3. The following examples borrowed from [14,9] tell us that one cannot get a complete analog to Theorem 3.3 for the non-commutative case. We also remark that Example 3.9(c) below tells us that a similar conclusion of [21, Theorem 18] for orthogonally additive and doubly orthogonality preserving holomorphic functions does not hold for zero product preserving ones.…”
Section: Orthogonally Additive and Zero Product Preserving Holomorphimentioning
confidence: 99%
“…Note however that without the conformal assumption we might not have a positive result, as Example 3.9 demonstrates. 9) or…”
Section: Orthogonally Additive and Zero Product Preserving Holomorphimentioning
confidence: 99%
See 2 more Smart Citations