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

• Autorzy: Oleg Reinov , Qaisar Latif
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s -numbers, Kolmogorov numbers, entropy numbers, etc. of operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 102
• Numer: 1
• Strony: 189-195

Daty

wydano

2014

Twórcy

autor

Oleg Reinov

• Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskii pr. 28, 198504 St. Petersburg, Russia

autor

Qaisar Latif

• Abdus Salam School of Mathematical Sciences, 68-B, New Muslim Town, Lahore 54600, Pakistan

Identyfikatory

DOI

10.4064/bc102-0-13