대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권3호
  • /
  • Pages.821-835
  • /
  • 2023
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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GENERALIZED (C, r)-HANKEL OPERATOR AND (R, r)-HANKEL OPERATOR ON GENERAL HILBERT SPACES

  • Jyoti Bhola (Department of Mathematics Hansraj College University of Delhi) ;
  • Bhawna Gupta (Department of Mathematics Netaji Subhas University of Technology)
  • 투고 : 2022.09.30
  • 심사 : 2023.04.13
  • 발행 : 2023.07.31
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초록

Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number r, the r-Hankel operators on a Hilbert space 𝓗 define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely kth-order (C, r)-Hankel operators and kth-order (R, r)-Hankel operators (k ≥ 2) which are closely related to r-Hankel operators in such a way that a kth-order (C, r)-Hankel matrix is formed from rk-Hankel matrix on deleting every consecutive (k - 1) columns after the first column and a kth-order (R, rk)-Hankel matrix is formed from r-Hankel matrix if after the first column, every consecutive (k - 1) columns are deleted. For |r| ≠ 1, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.

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과제정보

The authors are grateful to the referees for their valuable suggestions and comments which helped them in improving the manuscript.

참고문헌

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