Linear maps preserving the Lorentz-cone spectrum in certain subspaces of M-n

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Bueno, MI (Author) Other; Susana Borges Furtado (Author) FEP; Sivakumar, KC (Author) Other

Journal

Title: BANACH JOURNAL OF MATHEMATICAL ANALYSIS

Vol. 15 No. 3

ISSN: 2662-2033

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00V-50D

DOI: 10.1007/s43037-021-00140-y

Abstract (EN): In this paper, we completely characterize the linear maps phi : M -> M that preserve the Lorentz-cone spectrum, when M is one of the following subspaces of the space M-n of n x n real matrices: the subspace of diagonal matrices, the subspace of block-diagonal matrices A circle plus [a], where A is an element of Mn-1 is symmetric, and the subspace of block-diagonal matrices A circle plus [a], where A is an element of Mn-1 is a generic matrix. In particular, we show that phi should be what we call a standard map, namely, a map of the form phi(A) = PAQ for all A is an element of M or phi(A) = PA(T)Q for all A is an element of M, for some matrices P, Q is an element of M-n. We then characterize the standard maps preserving the Lorentz-cone spectrum, when M is the subspace S-n of symmetric matrices. The case MIMn was considered in a recent paper by Seeger (LAA 2020). We include it here for completeness.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20