Grothendieck–Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces
Volume 102 / 2014
Banach Center Publications 102 (2014), 189-195
MSC: Primary 47B06.
DOI: 10.4064/bc102-0-13
Abstract
Generalizing A. Grothendieck's (1955) and V. B. Lidskiĭ's (1959) trace formulas, we have shown in a recent paper that for $p\in[1,\infty]$ and $s\in (0,1]$ with $1/s=1+|1/2-1/p|$ and for every $s$-nuclear operator $T$ in every subspace of any $L_p(\nu)$-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 $L_p$-spaces.
