Open AccessOn block diagonal majorization and basic sequences
Author(s) -
Ali Bayati Eshkaftaki,
Noha Eftekhari
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2115101e
Subject(s) - mathematics , diagonal , majorization , block (permutation group theory) , bounded function , combinatorics , block matrix , operator (biology) , diagonal matrix , matrix (chemical analysis) , discrete mathematics , mathematical analysis , geometry , eigenvalues and eigenvectors , biochemistry , physics , chemistry , materials science , repressor , quantum mechanics , transcription factor , composite material , gene
In this paper we generalize (finite) block diagonal matrices to infinite dimensions and then by using block diagonal row stochastic matrices (as a special case), we define the relation < bdr on c0, which is said block diagonal majorization. We also obtain some important properties of Pbdr, the set of all bounded linear operators T : c0 ? c0; which preserve < bdr : Further, it is obtained necessary conditions for a bounded linear operator T on c0 to be a preserver of the block diagonal majorization < bdr. Also, the notion of the basic sequences correspond to block diagonal row stochastic matrices with description of some relevant examples will be discussed.