Subnormality for arbitrary powers of 2-variable weighted shifts whose restrictions to a large invariant subspace are tensor products

Authors

• Raúl E. Curto, University of Iowa
• Sang Hoon Lee, Chungnam National University
• Jasang Yoon, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

1-15-2012

Abstract

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 ℓ2(Z+2) with canonical orthonormal basis {e(k1,k2)}k1,k2≥0. The core of a commuting 2-variable weighted shift T, c(T), is the restriction of T to the invariant subspace generated by all vectors e(k1,k2) with k1, k2≥1; we say that c(T) is of tensor form if it is unitarily equivalent to a shift of the form (I⊗Wα, Wβ⊗I), where Wα and Wβ are subnormal unilateral weighted shifts. Given a 2-variable weighted shift T whose core is of tensor form, we prove that LPCS is solvable for T if and only if LPCS is solvable for any power T(m,n):=(T1^m,T2ⁿ) (m, n≥1). © 2011 Elsevier Inc.

Recommended Citation

Curto, Raúl E., Sang Hoon Lee, and Jasang Yoon. "Subnormality for arbitrary powers of 2-variable weighted shifts whose restrictions to a large invariant subspace are tensor products." Journal of Functional Analysis 262, no. 2 (2012): 569-583. https://doi.org/10.1016/j.jfa.2011.09.024

First Page

569

Last Page

583

Publication Title

Journal of Functional Analysis

DOI

10.1016/j.jfa.2011.09.024