Abstract
In this paper, we introduce the class of triangular n-isometric operators and study various properties. We show that every triangular n-isometric operator is subscalar of order 2n; in particular, every isometric operator is subscalar of order two. Consequently, if the spectrum of a triangular n-isometric operator T has a nonempty interior in , then T has a nontrivial invariant subspace. We also examine the hyperinvariant subspace problem for triangular n-isometric operators. Some spectral properties of this class of operators are also presented.
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