[Les images spectrales de shifts pondérés à 2-variables]
Nous étudions les images spectrales de shifts pondérés à deux variables et (conjointement) hyponormaux possédant des composants commutants sousnormaux. À la différence de tous les résultats connus dans la théorie des shifts pondérés simples sousnormaux à deux variables, nous démontrons que le spectre essentiel de Taylor peut être déconnecté. Nous faisons cela en obtenant une condition suffisante simple qui garantit le caractère déconnecté de ce spectre, basée sur les normes des sections horizontales du shift. Nous montrons également que pour chaque il existe un shift pondéré k-hyponormal à deux variables dont le spectre essentiel de Taylor est déconnecté.
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 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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@article{CRMATH_2006__343_9_579_0,
author = {Curto, Ra\'ul E. and Yoon, Jasang},
title = {Spectral pictures of 2-variable weighted shifts},
journal = {Comptes Rendus. Math\'ematique},
pages = {579--584},
publisher = {Elsevier},
volume = {343},
number = {9},
year = {2006},
doi = {10.1016/j.crma.2006.09.024},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.09.024/}
}
TY - JOUR AU - Curto, Raúl E. AU - Yoon, Jasang TI - Spectral pictures of 2-variable weighted shifts JO - Comptes Rendus. Mathématique PY - 2006 SP - 579 EP - 584 VL - 343 IS - 9 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.09.024/ DO - 10.1016/j.crma.2006.09.024 LA - en ID - CRMATH_2006__343_9_579_0 ER -
%0 Journal Article %A Curto, Raúl E. %A Yoon, Jasang %T Spectral pictures of 2-variable weighted shifts %J Comptes Rendus. Mathématique %D 2006 %P 579-584 %V 343 %N 9 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.09.024/ %R 10.1016/j.crma.2006.09.024 %G en %F CRMATH_2006__343_9_579_0
Curto, Raúl E.; Yoon, Jasang. Spectral pictures of 2-variable weighted shifts. Comptes Rendus. Mathématique, Tome 343 (2006) no. 9, pp. 579-584. doi : 10.1016/j.crma.2006.09.024. http://www.numdam.org/articles/10.1016/j.crma.2006.09.024/
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⁎ Research partially supported by NSF Grants DMS-0099357 and DMS-0400741.
