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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 $L^2[0,\infty)$.
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참고문헌 (9)
참고문헌 신청
C. S. Kubrusly / 2011 / The Elements of Operator Theory / Birkhauser/Springer
C. S. Kubrusly / 2002 / Semigroups of operators: theory and applications / Optimization Software :145~157
C. S. Kubrusly / 2006 / Abstract wavelets generated by Hilbert space shift operators / Adv. Math. Sci. Appl 16(2):643~660
N. Levan / 2014 / Dual-shift decomposition and wavelets / Int. J. Wavelets Multiresolut. Inf. Process 12(2):15
N. Levan / 1996 / On a class of shifts and shift semigroups of nite multiplicities / Japan J. Indust. Appl. Math 13(1):93~105
C. S. Kubrusly / 2002 / Semigroups of operators: theory and applications / Optimization Software :145~157
C. S. Kubrusly / 2006 / Abstract wavelets generated by Hilbert space shift operators / Adv. Math. Sci. Appl 16(2):643~660
N. Levan / 2014 / Dual-shift decomposition and wavelets / Int. J. Wavelets Multiresolut. Inf. Process 12(2):15
N. Levan / 1996 / On a class of shifts and shift semigroups of nite multiplicities / Japan J. Indust. Appl. Math 13(1):93~105
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