Forms of biisometric operators and biorthogonality
Functional Analysis
2024-12-17 v2
Abstract
The paper proves two results involving a pair (A,B) of P-biisometric or (m,P)-biisometric Hilbert-space operators for arbitrary positive integer m and positive operator P. It is shown that if A and B are power bounded and the pair (A,B) is (m,P)-biisometric for some m, then it is a P-biisometric pair. The important case when P is invertible is treated in detail. It is also shown that if (A,B) is P-biisometric, then there are biorthogonal sequences with respect to the inner product <.;.>_P=<P.;.> that have a shift-like behaviour with respect to this inner product.
Keywords
Cite
@article{arxiv.2401.16790,
title = {Forms of biisometric operators and biorthogonality},
author = {B. P. Duggal and C. S. Kubrusly},
journal= {arXiv preprint arXiv:2401.16790},
year = {2024}
}