p-Adic quantum calculus and ideals of compact operators

Evgeny I. Zelenov

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arXiv · 2205.07977

p-Adic quantum calculus and ideals of compact operators

Evgeny I. Zelenov

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Abstract

The paper proposes a construction of a quantum differentiation operator defined on the spaces of complex-valued functions of $p$-adic argument, and taking values in the algebra of bounded operators on a Hilbert space. The properties of this operator are investigated. In particular, it is proved that the differentiation operator maps $p$-adic Besov spaces into Schatten-von Neumann ideals in the algebra of compact operators.

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BibTeX RIS

Evgeny I. Zelenov. 2022-05-12. p-Adic quantum calculus and ideals of compact operators. https://arxiv.org/abs/2205.07977

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