The norm of the sum of two projections
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- by Ivan Vidav PDF
- Proc. Amer. Math. Soc. 65 (1977), 297-298 Request permission
Abstract:
Let e and ${\mathbf {f}},{\mathbf {e}} + {\mathbf {f}} \ne 0$, be two projections of a ${C^\ast }$-algebra A. J. Duncan and P. J. Taylor have shown that $\left \| {{\mathbf {e}} + {\mathbf {f}}} \right \| = 1 + \left \| {{\mathbf {ef}}} \right \|$. In this paper an algebraic proof of this equality is given.References
- Chandler Davis, Separation of two linear subspaces, Acta Sci. Math. (Szeged) 19 (1958), 172–187. MR 98980
- J. Duncan and P. J. Taylor, Norm inequalities for $C^*$-algebras, Proc. Roy. Soc. Edinburgh Sect. A 75 (1975/76), no. 2, 119–129. MR 454647, DOI 10.1017/S0308210500017832
- P. R. Halmos, Two subspaces, Trans. Amer. Math. Soc. 144 (1969), 381–389. MR 251519, DOI 10.1090/S0002-9947-1969-0251519-5
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 65 (1977), 297-298
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9939-1977-0442703-6
- MathSciNet review: 0442703