منابع مشابه
The Lifting Problem for Hyponormal Pairs of Commuting Subnormal Operators
We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of RC, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality. Our tools include the use of 2-variable weighted...
متن کاملJointly Hyponormal Pairs of Commuting Subnormal Operators Need Not Be Jointly Subnormal
We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.
متن کاملHyponormality and Subnormality for Powers of Commuting Pairs of Subnormal Operators
Let H0 (resp. H∞) denote the class of commuting pairs of subnormal operators on Hilbert space (resp. subnormal pairs), and for an integer k ≥ 1 let Hk denote the class of k-hyponormal pairs in H0. We study the hyponormality and subnormality of powers of pairs in Hk. We first show that if (T1, T2) ∈ H1, the pair (T 2 1 , T2) may fail to be in H1. Conversely, we find a pair (T1, T2) ∈ H0 such tha...
متن کاملOn Commuting Differential Operators
The theory of commuting linear differential expressions has received a lot of attention since Lax presented his description of the KdV hierarchy by Lax pairs (P,L). Gesztesy and the present author have established a relationship of this circle of ideas with the property that all solutions of the differential equations Ly = zy, z ∈ C, are meromorphic. In this paper this relationship is explored ...
متن کاملEssentially Commuting Toeplitz Operators
For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1978
ISSN: 0019-2082
DOI: 10.1215/ijm/1256048844