Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces

Oleg Reinov, and Qaisar Latif. "Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces." Banach Center Publications 102.1 (2014): 189-195. <http://eudml.org/doc/282047>.

@article{OlegReinov2014,
abstract = {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 $L_p(ν)$-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.},
author = {Oleg Reinov, Qaisar Latif},
journal = {Banach Center Publications},
keywords = {approximation properties; -nuclear operators; eigenvalue distributions},
language = {eng},
number = {1},
pages = {189-195},
title = {Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces},
url = {http://eudml.org/doc/282047},
volume = {102},
year = {2014},
}

TY - JOUR
AU - Oleg Reinov
AU - Qaisar Latif
TI - Grothendieck-Lidskiĭ theorem for subspaces of quotients of $L_p$-spaces
JO - Banach Center Publications
PY - 2014
VL - 102
IS - 1
SP - 189
EP - 195
AB - 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 $L_p(ν)$-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.
LA - eng
KW - approximation properties; -nuclear operators; eigenvalue distributions
UR - http://eudml.org/doc/282047
ER -