Infinite dimensional restricted invertibility
نویسندگان
چکیده
منابع مشابه
Infinite Dimensional Restricted Invertibility
The 1987 Bourgain-Tzafriri Restricted Invertibility Theorem is one of the most celebrated theorems in analysis. At the time of their work, the authors raised the question of a possible infinite dimensional version of the theorem. In this paper, we will give a quite general definition of restricted invertibility for operators on infinite dimensional Hilbert spaces based on the notion of density ...
متن کاملThe Infinite Dimensional Restricted Invertibility Theorem
The 1987 Bourgain-Tzafriri Restricted Invertibility Theorem is one of the most celebrated theorems in analysis. At the time of their work, the authors raised the question of a possible infinite dimensional version of the theorem. In this paper, we will give a quite general definition of restricted invertibility for operators on infinite dimensional Hilbert spaces based on the notion of density ...
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An interesting result of Doyle and Hocking states that a topological n-manifold is invertible if and only if it is a homeomorphic image of the n-sphere S. We shall prove that the sphere of any infinite-dimensional normed space is invertible. We shall also discuss the invertibility of other infinite-dimensional objects as well as an infinite-dimensional version of the Doyle-Hocking theorem.
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15 صفحه اولRestricted Invertibility Revisited
Suppose that m,n ∈ N and that A : R → R is a linear operator. It is shown here that if k, r ∈ N satisfy k < r 6 rank(A) then there exists a subset σ ⊆ {1, . . . ,m} with |σ| = k such that the restriction of A to R ⊆ R is invertible, and moreover the operator norm of the inverse A−1 : A(R) → R is at most a constant multiple of the quantity √ mr/((r − k) ∑m i=r si(A) 2), where s1(A) > . . . > sm(...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2012
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2012.09.008