Tensor-splitting properties of $n$-inverse pairs of operators

Stepan Paul¹ ; Caixing Gu²

¹ Department of Mathematics University of California, Santa Barbara Santa Barbara, CA 93106, U.S.A.
² Department of Mathematics California Polytechnic State University San Luis Obispo, CA 93407, U.S.A.

Studia Mathematica, Tome 238 (2017) no. 1, pp. 17-36

Résumé

We study $n$-inverse pairs of operators on the tensor product of Banach spaces. In particular we show that an $n$-inverse pair of elementary tensors of operators on the tensor product of two Banach spaces can arise only from $l$- and $m$-inverse pairs of operators on the individual spaces. This gives a converse to a result of Duggal and Müller (2013), and proves a conjecture of the second named author (2015). Our proof uses techniques from algebraic geometry, which generalize to other relations among operators in a tensor product. We apply this theory to obtain results for $n$-symmetries in a tensor product as well.

Détail

DOI : 10.4064/sm8518-2-2017

Keywords: study n inverse pairs operators tensor product banach spaces particular n inverse pair elementary tensors operators tensor product banach spaces arise only l m inverse pairs operators individual spaces gives converse result duggal ller proves conjecture second named author proof uses techniques algebraic geometry which generalize other relations among operators tensor product apply theory obtain results n symmetries tensor product