Consistent invertibility and Weyl's theorem
نویسندگان
چکیده
منابع مشابه
Consistent in invertibility operators and SVEP
If S(X ) ⊂ B(X ), where B(X ) denotes the algebra of operators on a Banach space X , then A ∈ B(X ) is S(X ) consistent if AB ∈ S(X ) ⇐⇒ BA ∈ S(X ) for every B ∈ B(X ). SVEP is a powerful tool in determining the S(X ) consistency of operators A for various choices of the subset S(X ).
متن کاملRevisiting 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 کاملMetrization Theorem for Uniform Loops with the Invertibility Property
Dagmar Markechová 1,*, Peter Vrábel 1 and Beáta Stehlíková 2 1 Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 74 Nitra, Slovakia; [email protected] 2 Department of Informatics and Mathematics, Faculty of Economy and Business, Pan European University, SK-851 05 Bratislava, Slovakia; [email protected] * Correspondence:...
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 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: Journal of Mathematical Analysis and Applications
سال: 2010
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2010.03.023