A new collection of $n-$tuple operator inequalities

TL;DR

This paper introduces new bounds for the norm and numerical radius of sums of Hilbert space operators, expanding the theoretical framework and providing comparative insights with existing bounds.

Contribution

It presents a novel collection of bounds for operator sums, including bounds for the triangle inequality, operator matrices, and singular values, with comparative analysis.

Findings

New bounds for operator norms and numerical radius

Examples showing bounds are often incomparable with existing ones

Enhanced understanding of operator sum inequalities

Abstract

In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the existing literature using examples that demonstrate, in general, how our results are incomparable with the known bounds. Of particular interest are the treatment of the triangle inequality, the numerical radius of operator matrices, and singular value bounds for sums of operators.