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.
Original language | English |
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Title of host publication | Operator Theory |
Subtitle of host publication | Advances and Applications |
Publisher | Springer International Publishing |
Pages | 501-510 |
Number of pages | 10 |
DOIs | |
State | Published - 2017 |
Publication series
Name | Operator Theory: Advances and Applications |
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Volume | 259 |
ISSN (Print) | 0255-0156 |
ISSN (Electronic) | 2296-4878 |
Bibliographical note
Publisher Copyright:© 2017 Springer International Publishing.
Keywords
- Characterizations of Hilbert spaces
- Linear combinations of two additional projections
- Projections