Essentially hyponormal multiplication operators on the Dirichlet space
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DOI: 10.1007/s00013-016-1006-z
Abstract: On the Dirichlet space D, we show that there is a multiplier f of D such that $$M_f$$Mf is not essentially hyponormal, i.e. $$\pi (M_f)$$π(Mf) is not hyponormal in the Calkin algebra $$B(D)/\mathcal {K}(D)$$B(D)/K(D). read more here.
Keywords: dirichlet space; operators dirichlet; essentially hyponormal; multiplication operators ... See more keywords
Generalized Cesàro Operators on Dirichlet-Type Spaces
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DOI: 10.1007/s10473-022-0111-2
Abstract: In this note, we introduce and study a new kind of generalized Cesaro operators $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$ for… read more here.
Keywords: generalized ces; type spaces; operators dirichlet; dirichlet type ... See more keywords
Kernels and ranks of Hankel operators on the Dirichlet spaces
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DOI: 10.1016/j.jmaa.2018.02.002
Abstract: Abstract We consider Hankel operators and little Hankel operators on the Dirichlet space and pluriharmonic Dirichlet space of the unit ball. We first describe kernels of Hankel operators with pluriharmonic symbol. Next, we prove that… read more here.
Keywords: operators pluriharmonic; dirichlet space; operators dirichlet; hankel ... See more keywords