Disk-recurrent Operators and Their Properties

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Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

In this article, the new concept of disk-recurrent operators is introduced. We prove that an operator is disk-recurrent if and only if it has a dense set of diskrecurrent vectors. We prove that these operators can be found in infinite dimensional and also finite dimensional Banach spaces. In addition, we show that the operator T is disk-recurrent if and only if T n is disk-recurrent. We also observe that if the diskrecurrence of the direct sum of two operators is disk-recurrent, then any of them is disk-recurrent and we express some results about this.

Language:
Persian
Published:
Journal of Mathematical Culture and Thought, Volume:41 Issue: 2, 2023
Pages:
119 to 128
https://www.magiran.com/p2551896