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Jacobus J. Grobler

North-West University

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Studia Mathematica | 2008

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

Jacobus J. Grobler; Heinrich Raubenheimer

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.

Czechoslovak Mathematical Journal | 2016

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

Jacobus J. Grobler; Heinrich Raubenheimer; Andre Swartz

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.

Indagationes Mathematicae | 2014

Jensen’s and martingale inequalities in Riesz spaces

Jacobus J. Grobler

Positivity | 2010

Continuous stochastic processes in Riesz spaces: the Doob–Meyer decomposition

Jacobus J. Grobler

Positivity | 2011

Doob's optional sampling theorem in Riesz spaces

Jacobus J. Grobler

Journal of Mathematical Analysis and Applications | 2014

Quadratic Variation of Martingales in Riesz Spaces

Jacobus J. Grobler; Coenraad C.A. Labuschagne; Valeria Marraffa

Journal of Mathematical Analysis and Applications | 2014

The Kolmogorov–Čentsov theorem and Brownian motion in vector lattices

Jacobus J. Grobler

Journal of Mathematical Analysis and Applications | 2015

The Itô integral for Brownian motion in vector lattices: Part 2

Jacobus J. Grobler; Coenraad C.A. Labuschagne

Journal of Mathematical Analysis and Applications | 2014

Corrigendum to “The Kolmogorov–Čentsov theorem and Brownian motion in vector lattices” [J. Math. Anal. Appl. 410 (2014) 891–901]

Jacobus J. Grobler

Positivity | 2005

Operators Represented by Conditional Expectations and Random Measures

Jacobus J. Grobler; D. T. Rambane

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