Jasang Yoon

Jointly 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.

Disintegration-of-measure techniques for commuting multivariable weighted shifts

We employ techniques from the theory of disintegration of measures to study the Lifting Problem for commuting

Spectral pictures of 2-variable weighted shifts⁎

n

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

-tuples of subnormal weighted shifts. We obtain a new necessary condition for the existence of a lifting, and generate new pathology associated with bringing together the Berger measures associated to each individual weighted shift. For subnormal

Completion of Hankel partial contractions of extremal type

2

An answer to a question of A. Lubin: The lifting problem for commuting subnormals

-variable weighted shifts, we then find the precise relation between the Berger measure of the pair and the Berger measures of the shifts associated to horizontal rows and vertical columns of weights.

COMPLETION OF HANKEL PARTIAL CONTRACTIONS OF NON-EXTREMAL TYPE

Abstract We study the spectral pictures of (jointly) hyponormal 2-variable weighted shifts with commuting subnormal components. By contrast with all known results in the theory of subnormal single and 2-variable weighted shifts, we show that the Taylor essential spectrum can be disconnected. We do this by obtaining a simple sufficient condition that guarantees disconnectedness, based on the norms of the horizontal slices of the shift. We also show that for every k ⩾ 1 there exists a k-hyponormal 2-variable weighted shift whose horizontal and vertical slices have 1- or 2-atomic Berger measures, and whose Taylor essential spectrum is disconnected. To cite this article: R.E. Curto, J. Yoon, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

Aluthge Transforms of 2-Variable Weighted Shifts

The Lifting Problem for Commuting Subnormals (LPCS) asks for necessary and sufficient conditions for a pair of subnormal operators onHilbert 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 ` 2 (Z 2 ) with canonical orthonormal basis fe(k1;k2)gk1;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

Properties of mono-weakly hyponormal 2-variable weighted shifts

We find concrete necessary and sufficient conditions for the existence of contractive completions of Hankel partial contractions of size 4 × 4 in the extremal case. Along the way we introduce a new approach that allows us to solve, algorithmically, the contractive completion problem for 4 × 4 Hankel matrices. As an application, we obtain a concrete example of a partially contractive 4 × 4 Hankel matrix, which does not admit a contractive completion.

k-HYPONORMALITY OF MULTIVARIABLE WEIGHTED SHIFTS

In this paper, we give an answer to a long-standing open question on the lifting problem for commuting subnormals (due to A. Lubin): The subnormality for the sum of commuting subnormal operators does not guarantee the existence of commuting normal extensions.