Geodesic
The index for Fredholm elements in a Banach algebra via a trace II
Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 205-211
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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.
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.
DOI : 10.1007/s10587-016-0250-5
Classification : 46H05, 47A10, 47A53
Keywords: trace; index; Fredholm element 
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Grobler, Jacobus J.; Raubenheimer, Heinrich; Swartz, Andre. The index for Fredholm elements in a Banach algebra via a trace II. Czechoslovak Mathematical Journal, Tome 66 (2016) no. 1, pp. 205-211. doi: 10.1007/s10587-016-0250-5

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