Operator Equations Inducing Some Generalizations of Slant Hankel Operators

An extension of slant Hankel operator, namely, the k -th-order λ-slant Hankel operator on the Lebesgue space L 2 ( T n ) , where T is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2024, Vol.40 (8), p.2017-2036
Main Authors: Datt, Gopal, Gupta, Bhawna Bansal
Format: Article
Language:English
Subjects:
Algebra
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
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Summary:An extension of slant Hankel operator, namely, the k -th-order λ-slant Hankel operator on the Lebesgue space L 2 ( T n ) , where T is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially k -th-order λ-slant Hankel operators on L 2 ( T n ) .
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-024-3084-3