Boundedness of Biorthogonal Systems in Banach Spaces
نویسنده
چکیده
We prove that every Banach space that admits a Markushevich basis also admits a bounded Markushevich basis.
منابع مشابه
Stability of Spline-Type Systems in the Abelian Case
In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis oper...
متن کاملUniform Boundedness Principle for operators on hypervector spaces
The aim of this paper is to prove the Uniform Boundedness Principle and Banach-Steinhaus Theorem for anti linear operators and hence strong linear operators on Banach hypervector spaces. Also we prove the continuity of the product operation in such spaces.
متن کاملGeometry of Banach Spaces and Biorthogonal Systems
A separable Banach space X contains l1 isomorphically if and only if X has a bounded fundamental total wc∗0-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total wc∗0-biorthogonal system.
متن کاملLinear operators of Banach spaces with range in Lipschitz algebras
In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.
متن کاملOn Bases in Banach Spaces
We investigate various kinds of bases in infinite dimensional Banach spaces. In particular, we consider the complexity of Hamel bases in separable and non-separable Banach spaces and show that in a separable Banach space a Hamel basis cannot be analytic, whereas there are non-separable Hilbert spaces which have a discrete and closed Hamel basis. Further we investigate the existence of certain c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008