A remark on orthogonality and symmetry of operators in B(H)

作者：Turnsek Aleksej^*

来源：Linear Algebra and Its Applications, 2017, 535: 141-150.

DOI：10.1016/j.laa.2017.09.001

• Birkhoff-James orthogonality
• Hilbert space
• Linear bounded operator

If T and A are operators on a Hilbert space such that vertical bar vertical bar T + lambda A vertical bar vertical bar >= vertical bar vertical bar T vertical bar vertical bar for all real numbers lambda, then T is said to be r-orthogonal to A. We obtain necessary and sufficient conditions for this to be the case. As a consequence we characterize r left symmetric (left symmetric) and r-right symmetric (right symmetric) operators in B(H), where H is a real or complex Hilbert space.

• 出版日期2017-12-15