Revisiting the Bourgain-Tzafriri restricted invertibility theorem
نویسندگان
چکیده
منابع مشابه
Revisiting the Bourgain-tzafriri Restricted Invertibility Theorem
We will give some new techniques for working with problems surrounding the Bourgain-Tzafriri Restricted Invertibility Theorem. First we show that the parameters which work in the theorem for all ‖T‖ ≤ 2 √ 2 closely approximate the parameters which work for all operators. This yields a generalization of the theorem which simultaneously does restricted invertibility on a small partition of the ve...
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 ...
متن کاملAn Elementary Proof of the Restricted Invertibility Theorem *
We give an elementary proof of a generalization of Bourgain and Tzafriri’s Restricted Invertibility Theorem, which says roughly that any matrix with columns of unit length and bounded operator norm has a large coordinate subspace on which it is well-invertible. Our proof gives the tightest known form of this result, is constructive, and provides a deterministic polynomial time algorithm for fin...
متن کاملBourgain ’ s Theorem
Exercise 1. Show that distances between sets do not necessarily satisfy the triangle inequality. That is, it is possible that d(S1, S2) + d(S2, S3) > d(S1, S3) for some sets S1, S2 and S3. Exercise 2. Prove that d(x, y) ≥ d(S, x)− d(S, y) and thus d(x, y) ≥ |d(S, x)− d(S, y)|. Proof. Fix ε > 0. Let y′ ∈ S be such that d(y′, y) ≤ d(S, y) + ε (if S is a finite set, there is y′ ∈ S s.t. d(y, y′) =...
متن کاملInfinite 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Operators and Matrices
سال: 2009
ISSN: 1846-3886
DOI: 10.7153/oam-03-04