Journal of Operator Theory
Volume 81, Issue 1, Winter 2019 pp. 81-105.
Taylor spectra and common invariant subspaces through the Duggal and
generalized Aluthge transforms for commuting $n$-tuples of operators
Authors:
Jaewoong Kim (1), Jasang Yoon (2)
Author institution: (1) Department of Mathematics, Korea Military Academy, Seoul, 01805,
Korea
(2) School of Mathematical and Statistical Sciences, The University of
Texas Rio Grande Valley, Edinburg, Texas 78539, U.S.A.
Summary: In the first part of this paper, we introduce two notions of multivariable
Duggal transforms (toral and spherical), and study their basic properties
including hyponormality and norm-continuity. In the second part, we study
how the Taylor spectrum and Taylor essential spectrum of $2 $-variable
weighted shifts behave under the toral and spherical Duggal transforms
including generalized Aluthge transforms. In the last part, we investigate
nontrivial common invariant subspaces between the toral (respectively spherical)
Duggal transform and the original $n$-tuple of bounded operators with dense
ranges. We also study the sets of common invariant subspaces among them.
DOI: http://dx.doi.org/10.7900/jot.2017nov27.2210
Keywords: Duggal transforms, generalized Aluthge transforms, common
invariant subspaces, Taylor spectra, commuting $n$-tuples, $2$-variable
weighted shifts
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