Browsing Faculty of Natural and Agricultural Sciences by Author "22982477 - Labuschagne, Louis Ernst"
Now showing items 1-14 of 14
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A crossed product approach to Orlicz spaces
(London Mathematical Society, 2013)We show how the known theory of non-commutative Orlicz spaces for semifinite von Neumann algebras equipped with an faithful normal semifinite trace may be recovered using crossed product techniques. Then using this as a ... -
Dynamics on noncommutative Orlicz spaces
(Springer, 2020)Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. This complements earlier work [26] where we made a strong case for the assertion that statistical physics of regular ... -
A Helson-Szegö theorem for subdiagonal subalgebras with applications to Toeplitz operators
(Elsevier, 2013)We formulate and establish a noncommutative version of the well known Helson–Szegö theorem about the angle between past and future for subdiagonal subalgebras. We then proceed to use this theorem to characterise the ... -
Invariant subspaces for H2 spaces of σ-finite algebras
(London Mathematical Society, 2017)We show that a Beurling type theory of invariant subspaces of noncommutative H 2 spaces holds true in the setting of subdiagonal subalgebras of σ-finite von Neumann algebras. This extends earlier work by Blecher and ... -
Maximal ergodic inequalities for Banach function spaces
(Elsevier, 2016)We analyse the Transfer Principle, which is used to generate weak type maximal inequalities for ergodic operators, and extend it to the general case of σσ-compact locally compact Hausdorff groups acting measure-preservingly ... -
Multiplication operators on non-commutative spaces
(Elsevier, 2019)Boundedness and compactness properties of multiplication operators on quantum (non-commutative) function spaces are investigated. For endomorphic multiplication operators these properties can be characterized in the setting ... -
Multipliers on noncommutative Orlicz spaces
(Taylor & Francis, 2014)We establish very general criteria for the existence of multiplication operators between noncommutative Orlicz spaces L 0 (fM) and L 1 (fM). We then show that these criteria contain existing results, before going on to ... -
On applications of Orlicz spaces to statistical physics
(Springer, 2014)We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. The pair of Orlicz spaces we explicitly use are, respectively, ... -
On entropy for general quantum systems
(International Press, 2020)In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy ... -
On vector-valued characters for noncommutative function algebras
(Springer, 2020)Let A be a closed subalgebra of a C∗-algebra, that is a norm-closed algebra of Hilbert space operators. We generalize to such operator algebras several key theorems and concepts from the theory of classical function algebras. ... -
Outers for noncommutative Hp revisted
(Polskiej Akademii Nauk, Instytut Matematyczny, 2013)We continue our study of outer elements of the noncommutative Hp spaces associated with Arveson's subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, ... -
Ueda’s peak set theorem for general Von Neumann algebras
(AMS, 2018)We extend Ueda’s peak set theorem for subdiagonal subalgebras of tracial finite von Neumann algebras to σ-finite von Neumann algebras (that is, von Neumann algebras with a faithful state, which includes those on a separable ... -
Weighted noncommutative Banach function spaces
(Springer, 2019)We review the concept of a weighted noncommutative Banach function space. This concept constitutes a generalisation of the by now well-known theory of noncommutative Banach function spaces associated with a semifinite von ... -
Why are Orlicz spaces useful for statistical physics?
(Springer, 2016)We review a new formalism based on Orlicz spaces for the description of large regular statistical systems. Our presentation includes both classical and quantum systems. This approach has the advantage that statistical ...
