Generalizing A. Grothendieck’s (1955) and V. B. Lidskiĭ’s (1959) trace formulas, we have shown in a recent paper that for p ∈ [1,∞] and s ∈ (0,1] with 1/s = 1 + |1/2-1/p| and for every s-nuclear operator T in every subspace of any -space the trace of T is well defined and equals the sum of all eigenvalues of T. Now, we obtain the analogous results for subspaces of quotients (equivalently: for quotients of subspaces) of -spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-13, author = {Oleg Reinov and Qaisar Latif}, title = {Grothendieck-Lidski\u\i\ theorem for subspaces of quotients of $L\_p$-spaces}, journal = {Banach Center Publications}, volume = {102}, year = {2014}, pages = {189-195}, zbl = {1320.47018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-13} }
Oleg Reinov; Qaisar Latif. Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces. Banach Center Publications, Tome 102 (2014) pp. 189-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-13/