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

Tom 102 / 2014

Oleg Reinov, Qaisar Latif Banach Center Publications 102 (2014), 189-195 MSC: Primary 47B06. DOI: 10.4064/bc102-0-13

Streszczenie

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.

Autorzy

  • Oleg ReinovDepartment of Mathematics and Mechanics
    St. Petersburg State University
    Universitetskii pr. 28
    198504 St. Petersburg, Russia
    e-mail
  • Qaisar LatifAbdus Salam School of Mathematical Sciences
    68-B, New Muslim Town
    Lahore 54600, Pakistan
    e-mail

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