Kragujevac Journal of Mathematics
University of Kragujevac - Faculty of Science

Properties of (C, r)-Hankel Operators and (R, r)-Hankel Operators on Hilbert Spaces

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Authors: J. BHOLA AND B. GUPTA

DOI: 10.46793/KgJMat2506.873B

Abstract:

We introduce the operators which are generalizations of Hankel-type operators, called the (C,r)-Hankel operator and (R,r)-Hankel operator on general Hilbert spaces. Our main result is to obtain characterizations for a bounded operator on general Hilbert spaces to be a (C,r)-Hankel operator (or (R,r)-Hankel operator). We also discuss some algebraic properties like boundedness (for |r|≠1) of these operators and the relationship between them. Moreover, some characterizations for the commutativity of these operators are explored.

Keywords:

Hilbert space, r-Hankel operator, (C,r)-Hankel operator, (R,r)-Hankel operator, Hilbert-Schmidt operator.

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