2021/07/24 by Xiao Dong Chen, Xiao Chen, Jian-Jian Jiang +4
Computer Science · Mathematics · #47B02 #47B15 #47B40 #47B47 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Rings and Algebras (math.RA) #Spectral Theory in Mathematical Physics #math.FA #math.OA #math.RA #msc:47B02 #msc:47B15 #msc:47B40 #msc:47B47
paper · pdf · doi:10.48550/arxiv.2107.11603
10 pages
openalex publication_date 2021/07/24 · arxiv created 2021/08/23 · arxiv updated 2021/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this short article, we mainly prove that, for any spectral operator A of type m on a complex Hilbert space, if a bounded operator B lies in the collection of bounded linear operators that are in the k-centralizer of every bounded linear operator in the l-centralizer of A, where k\leqslant l is two arbitrary positive integers satisfying l\geqslant k as well as l\geqslant 2m+1, then B must belong to the von Neumann algebra generated by A and identity operator. This result generalizes a matrix commutator theorem proved by M. F. Smiley. For this aim, Smiley-type operators are defined and studied.