Stable and stabilizable means involving linear operator arguments

Abstract

In this paper we extend the stability and stabilizability concepts from the case that the variables are positive real numbers to the case that the variables are positive linear operators. Since the algebra of bounded linear operators is not commutative, such extension does not appear to be obvious. As applications, iterative operator algorithms, converging to some operator means, are discussed.

Keywords:

• operator means
• power operator means
• cross operator means
• stable operator means
• stabilizable operator means

AMS Subject Classifications:

• 47A63
• 47A64

View correction statement:

Stable and stabilizable means involving linear operator arguments

Acknowledgments

The author would like to express his gratitude to the anonymous referee for his/her interesting comments and suggestions that improved this paper.