关键词: norm, orthogonal projection, positive operator, spectral, block operator valued matrix}

Abstract: In this paper, some refinements of norm equalities and inequalities of combination of two orthogonal projections are established. We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space. Furthermore, we give necessary and sufficient conditions under which the norm of the above combination of orthogonal projections attains its optimal value.

Key words: norm, orthogonal projection, positive operator, spectral, block operator valued matrix}