Hankel operators between Köthe spaces

Year 2025, Volume: 54 Issue: 4, 1458 - 1469, 29.08.2025

Nazlı Doğan

https://doi.org/10.15672/hujms.1560752

Abstract

This paper is about the operators defined between Köthe spaces whose associated matrix is a Hankel matrix. After demonstrating how these operators are defined, the conditions for their continuity and compactness are given. It is shown that the backward and forward shift operators are mean ergodic and Cesáro bounded by establishing a relationship between the backward and forward shift operators and Hankel and Toeplitz operators on power series spaces.

Keywords

Hankel matrix , Köthe spaces , compact operators

References

• [1] L. Crone and W. Robinson, Diagonal maps and diameters in Köthe spaces Israel J. Math. 20, 13-22, 1975.
• [2] E. Dubinsky and D. Vogt, Complemented subspaces in tame power series spaces, Studia Mathematica, 93 (1), 71–85, 1989.
• [3] N. Doğan. Toeplitz Operators Defined Between Köthe Spaces, accepted by Filomat, ArXiv: 2312.13609.
• [4] P. Domański and M. Jasiczak, Toeplitz operators on the space of real analytic functions: the Fredholm property. Banach J. Math. Anal. 12 (1), 31-67, 2018.
• [5] M. Jasiczak, Toeplitz operators on the space of all entire functions. N.Y.J. Math. 26, 756–789, 2020.
• [6] T. Kalmes, D. Santacreu, Mean Ergodic Weighted Shifts on Köthe Echelon Spaces, Results in Mathematics 78 (5), 2023.
• [7] R. Meise and D. Vogt, Introduction to functional analysis, Clarendon Press, Oxford, 1997.