1Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A. 2Internal Box 209 School of Computer, Statistical and Mathematical Sciences North-West University Pvt. Bag X6001 2520 Potchefstroom, South Africa
Studia Mathematica, Tome 217 (2013) no. 3, pp. 265-287
We continue our study of outer elements of the noncommutative $H^p$ spaces associated with Arveson's subdiagonal algebras. We extend our generalized inner-outer factorization theorem, and our characterization of outer elements, to include the case of elements with zero determinant. In addition, we make several further contributions to the theory of outers. For example, we generalize the classical fact that outers in $H^p$ actually satisfy the stronger condition that there exist $a_n \in A$ with $h a_n \in {\rm Ball}(A)$ and $h a_n \to 1$ in $p$-norm.
Keywords:
continue study outer elements noncommutative spaces associated arvesons subdiagonal algebras extend generalized inner outer factorization theorem characterization outer elements include elements zero determinant addition make several further contributions theory outers example generalize classical outers actually satisfy stronger condition there exist ball p norm
Affiliations des auteurs :
David P. Blecher
1
;
Louis E. Labuschagne
2
1
Department of Mathematics University of Houston Houston, TX 77204-3008, U.S.A.
2
Internal Box 209 School of Computer, Statistical and Mathematical Sciences North-West University Pvt. Bag X6001 2520 Potchefstroom, South Africa
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David P. Blecher; Louis E. Labuschagne. Outers for noncommutative $H^{p}$ revisited. Studia Mathematica, Tome 217 (2013) no. 3, pp. 265-287. doi: 10.4064/sm217-3-4
