Refined Hilbert-Schmidt numerical radius inequalities

Key Points

• The aim is to establish new bounds for the Hilbert-Schmidt numerical radius of 2x2 operator matrices that improve upon existing results.
• Developed new inequalities for Hilbert-Schmidt numerical radius.
• Provided examples illustrating the superiority of the new bounds over existing ones.
• The new bounds are shown to be more accurate than previous inequalities.
• Several examples demonstrate the effectiveness of the refined bounds.