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Grothendieck-Lidskiĭ theorem for subspaces of quotients of L p -spaces

Oleg ReinovQaisar Latif — 2014

Banach Center Publications

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.

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