On the spectrum of multiplication operators

zbMath1424.47166arXiv1805.08553MaRDI QIDQ5383134

Lyudmyla Turowska, Viktor S. Shul'man

Publication date: 19 June 2019

Abstract: We study relations between spectra of two operators that are connected to each other through some intertwining conditions. As application we obtain new results on the spectra of multiplication operators on $B(clH)$ relating it to the spectra of the restriction of the operators to the ideal $mathcal{C}_2$ of Hilbert-Schmidt operators. We also solve one of the problems, posed in [B.Magajna, Proc. Amer. Math. Soc, 141 2013, 1349-1360] about the positivity of the spectrum of multiplication operators with positive operator coefficients when the coefficients on one side commute. Using the Wiener-Pitt phenomena we show that the spectrum of a multiplication operator with normal coefficients satisfying the Haagerup condition might be strictly larger than the spectrum of its restriction to $mathcal{C}_2$.

Full work available at URL: https://arxiv.org/abs/1805.08553

zbMATH Keywords

Hilbert-Schmidt operatorsintertwiningmultiplication operatorsspace of bounded linear operators

Mathematics Subject Classification ID

Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) Commutators, derivations, elementary operators, etc. (47B47) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Linear spaces of operators (47L05)

Related Items (3)

On associative spectra of operations ⋮ Classification and properties of the spectrum of additive operators ⋮ The spectrum of the product of operators, and the product of their numerical ranges

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