منابع مشابه
Commutators on L p , 1 ≤ p < ∞ †
The operators on Lp = Lp[0, 1], 1 ≤ p < ∞, which are not commutators are those of the form λI + S where λ , 0 and S belongs to the largest ideal in L(Lp). The proof involves new structural results for operators on Lp which are of independent interest.
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Let T be a bounded linear operator on X = (Σ `q)p with 1 ≤ q < ∞ and 1 < p <∞. Then T is a commutator if and only if for all non zero λ ∈ C, the operator T − λI is not X-strictly singular.
متن کاملON COMMUTATORS IN p-GROUPS
For a given prime p, what is the smallest integer n such that there exists a group of order p in which the set of commutators does not form a subgroup? In this paper we show that n = 6 for any odd prime and n = 7 for p = 2.
متن کاملp-SUMMABLE COMMUTATORS IN DIMENSION d
We show that many invariant subspaces M for d-shifts (S1, . . . , Sd) of finite rank have the property that the orthogonal projection PM onto M satisfies PMSk − SkPM ∈ L, 1 ≤ k ≤ d for every p > 2d, L denoting the Schatten-von Neumann class of all compact operators having p-summable singular value lists. In such cases, the d tuple of operators T̄ = (T1, . . . , Td) obtained by compressing (S1, ....
متن کاملCommutators on ` ∞
The operators on `∞ which are commutators are those not of the form λI + S with λ 6= 0 and S strictly singular.
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2012
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2012-00748-6