biisometric operators and biorthogonal sequences
Bull. Korean Math. Soc.
Published online 2019 May 16
Carlos Kubrusly and 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 basis are replaced with biorthogonal
sequences, and it is also shown how such a pair of biisometric operators
yield 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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