<i>L</i>(<i>n</i>)-HYPONORMALITY: A MISSING BRIDGE BETWEEN SUBNORMALITY AND PARANORMALITY

Jung, Il Bong; Park, Sun-Hyung; Stochel, Jan

doi:10.1017/s1446788710000091

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2017

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“…Motivated by these previous results and the criterion for subnormality of general unbounded operators due to Stochel and Szafraniec (see [27,Theorem 3]), we introduce in this paper classes S * n,r of unbounded operators closely related to cosubnormal operators (they resemble, in a sense, weak hyponormality classes studied in the case of bounded operators, cf. [22,20,15,19]) and investigate under what conditions composition operators with infinite matrix symbols belong to the classes. We use inductive limits to achieve our goal.…”

Section: Introductionmentioning

confidence: 99%

Unbounded composition operators via inductive limits: Cosubnormal operators with matrix symbols, II

Budzyński¹,

Dymek²,

Płaneta³

2017

Banach J. Math. Anal.

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The paper deals with unbounded composition operators with infinite matrix symbols acting in L 2 -spaces with respect to the gaussian measure on R ∞ . We introduce weak cohyponormality classes S * n,r of unbounded operators and provide criteria for the aforementioned composition operators to belong to S * n,r . Our approach is based on inductive limits of operators.2010 Mathematics Subject Classification. Primary 47B33, 47B37; secondary 47A05, 28C20. Key words and phrases. Composition operator in L 2 -space, inductive limits of operators, subnormal operators.

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