On spectral continuity of positive elements

• Autorzy: S. Mouton
• Języki publikacji: EN

Abstrakty

EN

Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the above inequalities.

Kategorie tematyczne

• 47B65: Positive operators and order-bounded operators
• 06F25: Ordered rings, algebras, modules
• 46H05: General theory of topological algebras
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 174
• Numer: 1
• Strony: 75-84

Daty

wydano

2006

Twórcy

autor

S. Mouton

• Department of Mathematics, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa

Identyfikatory

DOI

10.4064/sm174-1-6