This paper's main objective is to find new upper bounds for the norm of the sum of two Hilbert space operators and their Kronecker product. The obtained results extend some previously known results from the set of positive operators to arbitrary ones and refine several existing bounds. In particular, applications of the established bounds include refining celebrated numerical radius inequalities and the celebrated operator Cauchy–Schwarz norm inequality.
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Sababheh et al. (2024) studied this question.
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