# Grothendieck-Lidskiĭ theorem for subspaces of quotients of ${L}_{p}$-spaces

Banach Center Publications (2014)

- Volume: 102, Issue: 1, page 189-195
- ISSN: 0137-6934

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topOleg 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 -

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