The index for Fredholm elements in a Banach algebra via a trace II

We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity...

Full description

Saved in:
Bibliographic Details
Published inCzechoslovak mathematical journal Vol. 66; no. 1; pp. 205 - 211
Main Authors Grobler, Jacobus J., Raubenheimer, Heinrich, Swartz, Andre
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016
Subjects
Analysis
Convex and Discrete Geometry
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
index
trace
47A53
47A10
Fredholm element
46H05
Online AccessGet full text

Cover

More Information
Summary:We show that the index defined via a trace for Fredholm elements in a Banach algebra has the property that an index zero Fredholm element can be decomposed as the sum of an invertible element and an element in the socle. We identify the set of index zero Fredholm elements as an upper semiregularity with the Jacobson property. The Weyl spectrum is then characterized in terms of the index.
ISSN:0011-4642
1572-9141
DOI:10.1007/s10587-016-0250-5