@inbook{f5eaad31fc3944eea5660cfbaa30a41b,

title = "On the norm of linear combinations of projections and some characterizations of Hilbert spaces",

abstract = "Let B be a Banach space and let P,Q (P,Q ≠ 0) be two complementary projections in B (i.e., P + Q = I). For dimB > 2 we show that formulas of the kind ||aP + bQ|| = f(a, b, ||P||) hold if and only if the norm in B can be induced by an inner product. The two-dimensional case needs special consideration which is done in the last two sections.",

keywords = "Characterizations of Hilbert spaces, Linear combinations of two additional projections, Projections",

author = "Nahum Krupnik and Alexander Markus",

note = "Publisher Copyright: {\textcopyright} 2017 Springer International Publishing.",

year = "2017",

month = jan,

day = "1",

doi = "10.1007/978-3-319-49182-0_20",

language = "English",

series = "Operator Theory: Advances and Applications",

publisher = "Springer International Publishing",

pages = "501--510",

booktitle = "Operator Theory",

}