A Cyclic Subnormal Completion of Complex Data
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초록
For a finite subset Λ of N0 × N0, where N0 is theset of nonnegative integers, we say that a complex data γΛ := {γij}(i,j) ∈ Λ in the unit disc D of complex numbers has a cyclicsubnormal completion if there exists a Hilbert space H and a cyclic subnormal operator S on H with a unit cyclic vector x0 ∈ H such that <S*iSjx0, x0> = γij for all i,j ∈ N0. In this note, we obtain some sufficient conditions for acyclic subnormal completion of γΛ, where Λ is a finite subset of N0 × N0.
Abstract
For a finite subset Λ of N0 × N0, where N0 is theset of nonnegative integers, we say that a complex data γΛ := {γij}(i,j) ∈ Λ in the unit disc D of complex numbers has a cyclicsubnormal completion if there exists a Hilbert space H and a cyclic subnormal operator S on H with a unit cyclic vector x0 ∈ H such that <S*iSjx0, x0> = γij for all i,j ∈ N0. In this note, we obtain some sufficient conditions for acyclic subnormal completion of γΛ, where Λ is a finite subset of N0 × N0.
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