Condition pseudospectral radius of bounded linear operators

ABSTRACT

In this article, we consider the condition pseudospectrum of bounded linear operators on a Banach space. The condition pseudospectrum of normal matrices and Jordan blocks are characterized and condition pseudospectral radius of the classes are found. Sub-additivity and sub-multiplicativity of the condition pseudospectral radius for commuting pairs of bounded linear operators are proved. It is shown that the condition pseudospectral radius becomes a complete algebra norm in a commutative complex unital Banach algebra. Certain examples are given to illustrate the results. The results developed are also extended to a general setting.

Keywords:

• Spectrum
• spectral radius
• condition pseudospectrum
• commutativity
• sub-additivity
• sub-multiplicativity

2010 Mathematics Subject Classifications:

• Primary 47A10
• Secondary 15A09
• 47A25
• 47A30

Disclosure statement

No potential conflict of interest was reported by the authors.