•  
  •  
 

Keywords

Weak supermajorization, Linear preserver, Doubly superstochastic, Permutation

Abstract

Linear preservers of weak supermajorization which is defined on positive functions contained in the discrete Lebesgue space $\ell^1(I)$ are characterized. Two different classes of operators that preserve the weak supermajorization are formed. It is shown that every linear preserver may be decomposed as sum of two operators from the above classes, and conversely, the sum of two operators which satisfy an additional condition is a linear preserver. Necessary and sufficient conditions under which a bounded linear operator is a linear preserver of the weak supermajorization are given. It is concluded that positive linear preservers of the weak supermajorization coincide with preservers of weak majorization and standard majorization on $\ell^1(I)$.

abs_vol34_pp407-427.pdf (123 kB)
Abstract

Share

COinS
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.