Biisometric operators and biorthogonal sequences
Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 585-596
Published online May 16, 2019
Printed May 31, 2019
Carlos Kubrusly, Nhan Levan
Federal University; University of California
Abstract : It is shown that a pair of Hilbert space operators $V$ and $W$ such that ${V^*W=I}$ (called a biisometric pair) shares some common properties with unilateral shifts when orthonormal bases are replaced with biorthogonal sequences, and it is also shown how such a pair of biisometric operators yields a pair of biorthogonal sequences which are shifted by them. These are applied to a class of Laguerre operators on $L^2[0,\infty)$.
Keywords : biisometric operators, biorthogonal sequences, unilateral shifts, Hilbert spaces
MSC numbers : 42C05, 47B37
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