On connection between the norm of a sum of orthoprojections onto subspaces and the norm of the product of orthoprojections onto the corresponding orthogonal complements

• Datum: 2015
• Hauptverfasser: Rabanovich, V. I., Рабанович, В. I.
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Інститут математики НАН України 2015
• Online Zugang: https://trim.imath.kiev.ua/index.php/trim/article/view/13
• Назва журналу: Transactions of Institute of Mathematics of NAS of Ukraine

We show that if $\epsilon I \le P_1+P_2+\dots+P_k $, where $I$ is the identity operator and $P_1,\dots, P_k$ are orthoprojections that project onto linearly independent subspaces, then the norm $\|P_1+P_2+\dots+P_k\|\le k-(k-1)\epsilon$. It was fou...