Subnormality of 2-variable weighted shifts with diagonal core Subnormality of 2-variable weighted shifts with diagonal core ⋆
نویسندگان
چکیده
The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for a pair of subnormal operators on Hilbert space to admit commuting normal extensions. Given a 2-variable weighted shift T with diagonal core, we prove that LPCS is soluble for T if and only if LPCS is soluble for some power Tm (m ∈ Z+,m ≡ (m1,m2),m1,m2 ≥ 1). We do this by first developing the basic properties of diagonal cores, and then analyzing how a diagonal core interacts with the rest of the 2-variable weighted shift.
منابع مشابه
Subnormality for arbitrary powers of 2-variable weighted shifts whose restrictions to a large invariant subspace are tensor products
The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for a pair of subnormal operators on Hilbert space to admit commuting normal extensions. We study LPCS within the class of commuting 2-variable weighted shifts T ≡ (T1, T2) with subnormal components T1 and T2, acting on the Hilbert space l (Z+) with canonical orthonormal basis {e(k1,k2)}k1,k2≥0 . Th...
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