On the differentiability of the norm in trace classes S p
Séminaire Maurey-Schwartz (1974-1975), Exposé no. 22, 8 p. 
@article{SAF_1974-1975____A21_0,
     author = {Tomczak-Jaegermann, N.},
     title = {On the differentiability of the norm in trace classes $S_p$},
     journal = {S\'eminaire Maurey-Schwartz},
     note = {talk:22},
     pages = {1--8},
     publisher = {Ecole Polytechnique, Centre de Math\'ematiques},
     year = {1974-1975},
     zbl = {0311.47007},
     language = {en},
     url = {http://www.numdam.org/item/SAF_1974-1975____A21_0/}
}
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Tomczak-Jaegermann, N. On the differentiability of the norm in trace classes $S_p$. Séminaire Maurey-Schwartz (1974-1975), Exposé no. 22, 8 p. http://www.numdam.org/item/SAF_1974-1975____A21_0/

[1] R. Bonic and J. Frampton: Smooth functions on Banach manifolds. J. of Math. and Mech. 15 (1966) pp.877-898. | MR | Zbl

[2] I.C. Gohberg and M.G. Krein: Introduction to the theory of linear non-selfadjoint operators in Hilbert space. Moscow 1965 (in Russian) | MR