Quadratic Weighted Geometric Mean in Hermitian Unital Banach Star-Algebras
Silvestru Sever Dragomir
TL;DR
This paper introduces a quadratic weighted geometric mean for invertible elements in Hermitian unital Banach star-algebras and establishes related inequalities under different conditions.
Contribution
It defines a new mean for elements in Banach star-algebras and derives inequalities, expanding the mathematical understanding of such structures.
Findings
Defined quadratic weighted geometric mean for invertible elements
Established inequalities for the mean under various assumptions
Extended classical mean inequalities to Banach star-algebra context
Abstract
In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved.
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Taxonomy
TopicsMathematical Inequalities and Applications · Holomorphic and Operator Theory · Advanced Operator Algebra Research