کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4589581 | 1334888 | 2016 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
The Lidskii trace property and the nest approximation property in Banach spaces
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: The Lidskii trace property and the nest approximation property in Banach spaces The Lidskii trace property and the nest approximation property in Banach spaces](/preview/png/4589581.png)
چکیده انگلیسی
For a Banach space X, the Lidskii trace property is equivalent to the nest approximation property; that is, for every nuclear operator on X that has summable eigenvalues, the trace of the operator is equal to the sum of the eigenvalues if and only if for every nest NN of closed subspaces of X, there is a net of finite rank operators on X , each of which leaves invariant all subspaces in NN, that converges uniformly to the identity on compact subsets of X . The Volterra nest in Lp(0,1)Lp(0,1), 1≤p<∞1≤p<∞, is shown to have the Lidskii trace property. A simpler duality argument gives an easy proof of the result [2, Theorem 3.1] that an atomic Boolean subspace lattice that has only two atoms must have the strong rank one density property.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 271, Issue 3, 1 August 2016, Pages 566–576
Journal: Journal of Functional Analysis - Volume 271, Issue 3, 1 August 2016, Pages 566–576
نویسندگان
T. Figiel, W.B. Johnson,