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Spectral pictures of 2-variable weighted shifts

Raul E. Curto·Jasang Yoon
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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.

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Raul E. Curto, Jasang Yoon. 2006-10-29. Spectral pictures of 2-variable weighted shifts. https://doi.org/10.1016/j.crma.2006.09.024

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