Open AccessThe minus order for projections
Author(s) -
Yuan Li,
Jiajia Niu,
Xiaoming Xu
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2108761l
Subject(s) - mathematics , infimum and supremum , projection (relational algebra) , order (exchange) , hilbert space , combinatorics , orthographic projection , set (abstract data type) , mathematical analysis , geometry , algorithm , finance , economics , computer science , programming language
Let B(H)Id be the set of all projections on a Hilbert space H. The necessary and sufficient conditions are presented for the existence of the supremum, as well as the infimum, of two arbitrary projections in B(H)Id with respect to the minus order ?. For a projection Q in B(H)Id; the properties of the sets {P : P is an orthogonal projection on H and Q ? P} and {P : P is an orthogonal projection on H and P ? Q} are further explored.