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arXiv · 2401.16790

Forms of biisometric operators and biorthogonality

B. P. Duggal·C. S. Kubrusly
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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= that have a shift-like behaviour with respect to this inner product.

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B. P. Duggal, C. S. Kubrusly. 2024-01-30. Forms of biisometric operators and biorthogonality. https://arxiv.org/abs/2401.16790

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