On the spectrum and spectrum multiplicities of a sum of orthogonal projections

• Published in: Algebra and Discrete Mathematics
• Date: 2004
• Main Authors: Kyrychenko, A.A., Samoılenko, Yu.S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2004
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/156422
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On the spectrum and spectrum multiplicities of a sum of orthogonal projections / A.A. Kyrychenko, Yu.S. Samoılenko // Algebra and Discrete Mathematics. — 2004. — Vol. 3, № 3. — С. 71–76. — Бібліогр.: 9 назв. — англ.

Let H be a unitary (finite dimensional Hilbert) space. It is known [1] that a self-adjoint operator on H, A = A* ≥ 0, is a sum of n orthogonal projections for some n ∈ N if and only if 1) tr A ∈ N∪{0}, 2) tr A ≥ dim Im A (Im A = AH)