Tensor-splitting properties of $n$-inverse pairs of operators
Volume 238 / 2017
Studia Mathematica 238 (2017), 17-36
MSC: Primary 47A80,47A10; Secondary 47B47.
DOI: 10.4064/sm8518-2-2017
Published online: 20 April 2017
Abstract
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.
