A geometric interpretation of Segal’s inequality $\Vert e^ {X+Y}\Vert \leq \Vert e^ {X/2}e^ Ye^ {X/2}\Vert$
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- by G. Corach, H. Porta and L. Recht PDF
- Proc. Amer. Math. Soc. 115 (1992), 229-231 Request permission
Abstract:
It is shown that the exponential mapping of the manifold of positive elements of a ${C^*}$-algebra (provided with its natural connection) increases distances (when measured in the natural Finsler structure). The proof relies on Segal’s inequality $||{e^{X + Y}}|| \leq ||{e^{X/2}}{e^Y}{e^{X/2}}||$, valid for all symmetric $X,Y$ in any ${C^*}$-algebra. In turn, this geometric inequality implies Segal’s’ inequality.References
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G. Corach, H. Porta, and L. Recht, The geometry of the space of self-adjoint invertible elements of a ${C^*}$-algebra, preprint form in Trabajos de Matemática no. 149, Instituto Argentino de Matemática, December 1989.
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 229-231
- MSC: Primary 46L99; Secondary 58B20
- DOI: https://doi.org/10.1090/S0002-9939-1992-1075945-8
- MathSciNet review: 1075945