Maps Preserving Schatten $p$-Norms of Convex Combinations

作者: David Li-Wei Kuo , Ming-Cheng Tsai , Ngai-Ching Wong , Jun Zhang

DOI: 10.1155/2014/520795

关键词:

摘要: We study maps of positive operators the Schatten -classes (), which preserve -norms convex combinations, that is, . They are exactly those carrying form for a unitary or antiunitary In case , we have same conclusion whenever it just holds all Hilbert-Schmidt class norm Some examples demonstrated.

参考文章(14)
Lajos Molnár, An algebraic approach to Wigner's unitary-antiunitary theorem Journal of The Australian Mathematical Society. ,vol. 65, pp. 354- 369 ,(1998) , 10.1017/S144678870003593X
Theagenis J. Abatzoglou, Norm Derivatives on Spaces of Operators. Mathematische Annalen. ,vol. 239, pp. 129- 135 ,(1979) , 10.1007/BF01420370
Bernard Russo, Isometries of the trace class Proceedings of the American Mathematical Society. ,vol. 23, pp. 213- ,(1969) , 10.1090/S0002-9939-1969-0247491-X
F. J. Yeadon, Isometries of non-commutative Lp-spaces Mathematical Proceedings of the Cambridge Philosophical Society. ,vol. 90, pp. 41- 50 ,(1981) , 10.1017/S0305004100058515
Chi-Kwong Li, Stephen Pierce, Linear Preserver Problems American Mathematical Monthly. ,vol. 108, pp. 591- 605 ,(2001) , 10.1080/00029890.2001.11919790
Studies in mathematical physics D. Reidel Publishing Company. ,(1973) , 10.1007/978-94-010-2669-7
Jor-Ting Chan, Chi-Kwong Li, Nung-Sing Sze, Isometries for unitarily invariant norms Linear Algebra and its Applications. ,vol. 399, pp. 53- 70 ,(2005) , 10.1016/J.LAA.2004.05.017
Gianni Cassinelli, Ernesto de Vito, Pekka J. Lahti, Alberto Levrero, Symmetry Groups in Quantum Mechanics and the Theorem of Wigner on the Symmetry Transformations Reviews in Mathematical Physics. ,vol. 09, pp. 921- 941 ,(1997) , 10.1142/S0129055X97000324