Another unitarily invariant norm attaining the minimum norm bound for commutators
نویسندگان
چکیده
منابع مشابه
Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm
Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest per...
متن کاملBergman Commutators and Norm Ideals
Let P be the orthogonal projection from L(B, dv) onto the Bergman space La(B, dv) of the unit ball in C . In this paper we characterize the membership of commutators of the form [Mf , P ] in the norm ideal CΦ, where the symmetric gauge function Φ is allowed to be arbitrary.
متن کاملDenseness for norm attaining operator-valued functions
In this note we offer a short, constructive proof for Hilbert spaces of Lindenstrauss’ famous result on the denseness of norm attaining operators. Specifically, we show given any A ∈ L(H) there is a sequence of rank-1 operators Kn such that A+Kn is norm attaining for each n and Kn converges in norm to zero. We then apply our construction to establish denseness results for norm attaining operato...
متن کاملOn the Minimum Norm
This paper describes a new technique to nd the minimum norm solution of a linear program. The main idea is to reformulate this problem as an unconstrained minimization problem with a convex and smooth objective function. The minimization of this objective function can be carried out by a Newton-type method which is shown to be globally convergent. Furthermore, under certain assumptions, this Ne...
متن کاملNorm Attaining Multilinear Forms on L1(μ)
Given an arbitrary measure μ, this study shows that the set of norm attaining multilinear forms is not dense in the space of all continuous multilinear forms on L1 μ . However, we have the density if and only if μ is purely atomic. Furthermore, the study presents an example of a Banach space X in which the set of norm attaining operators from X into X∗ is dense in the space of all bounded linea...
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: Linear Algebra and its Applications
سال: 2010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.06.037