On Generalized Powers of Operators
Ahmed Bachir, Mohammed Hichem Mortad, Nawal Ali Sayyaf
TL;DR
This paper introduces a novel concept of generalized powers of linear operators, where operators are raised to other operators instead of numbers, and explores their fundamental properties.
Contribution
It presents the first formal definition of operator-to-operator powers and investigates their basic properties and implications.
Findings
Defined generalized powers of operators.
Analyzed properties of these operator powers.
Established foundational results for future research.
Abstract
In this note, we introduce generalized powers of linear operators. More precisely, operators are not raised to numbers but to other operators. We discuss several properties as regards this notion.
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Taxonomy
TopicsMatrix Theory and Algorithms