Biisometric operators and biorthogonal sequences
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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 $L^2[0,\infty)$.
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 $L^2[0,\infty)$.
참고문헌 (9)
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