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Operator Theory Seminar - Professor Raúl Curto; Department of Mathematics, University of Iowa
Oct 8, 2024
01:30 PM - 02:30 PM
30 North Dubuque Street, Iowa City, IA 52242
Semihyponormality of Commuting Pairs of Hilbert Space Operators
Professor Raúl Curto; Department of Mathematics, University of Iowa
We will first describe an explicit formula for the square root of positive 2 x 2 operator matrices with commuting entries, and then use it to define and study semi-hyponormality for commuting pairs of Hilbert space operators. For the well-known 3-parameter family W_(α, β) (a, x, y) of 2-variable weighted shifts, we have been able to completely identify the parametric regions in the open unit cube where W_(α, β) (a, x, y) is subnormal, hyponormal, semi- hyponormal, and weakly hyponormal. As a result, we describe in detail concrete sub-regions where, for instance, weak hyponormality holds but semi- hyponormality does not hold. To accomplish this, we employ a new technique emanating from the homogeneous orthogonal decomposition of l²(Z²+). The talk is based on joint work with Jasang Yoon (The University of Texas Rio Grande Valley).
To participate in this seminar remotely via Zoom, go to https://uiowa.zoom.us/j/95316149275
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