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The Scattered Range Problem of Elementary Operators on B(H)
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作者 Peng CAO Cun WANG 《Acta Mathematica Sinica,English Series》 SCIE 2024年第11期2684-2692,共9页
A scattered operator is a bounded linear operator with at most countable spectrum.In this paper,we prove that for any elementary operator on B(H),not only for finite length but also for infinite length,if the range of... A scattered operator is a bounded linear operator with at most countable spectrum.In this paper,we prove that for any elementary operator on B(H),not only for finite length but also for infinite length,if the range of the elementary operator is contained in scattered operators,then the corresponding sum of multipliers is a compact operator.We also prove that for some special classes of elementary operators,such as the elementary operators of length 2,higher order inner derivations and generalized inner derivation,if the range of the elementary operator is contained in the set of scattered operators,then the range is contained in the set of power compact operators.At the same time,the multipliers of the corresponding elementary operators are characterized. 展开更多
关键词 Compact operator elementary operator inner derivation scattered element
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