Schauder bases under uniform renormings
نویسنده
چکیده
Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. Mathematics Subject Classification (2000). 46B03.
منابع مشابه
Almost Transitive and Maximal Norms in Banach Spaces
We prove that the spaces `p, 1 < p < ∞, p 6= 2, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almosttransitive renormings. This answers a problem posed by Deville, Godefroyand Zizler in 1993. We obtain this as a consequence of a new property ofalmost transitive spaces with a Schauder basis, namely we prove that in suchspaces the unit...
متن کاملWeaving Schauder frames
We extend the concept of weaving Hilbert space frames to the Banach space setting. Similar to frames in a Hilbert space, we show that for any two approximate Schauder frames for a Banach space, every weaving is an approximate Schauder frame if and only if there is a uniform constant C ≥ 1 such that every weaving is a C-approximate Schauder frame. We also study weaving Schauder bases, where it i...
متن کاملGabor Schauder Bases and the Balian–low Theorem
The Balian–Low Theorem is a strong form of the uncertainty principle for Gabor systems which form orthonormal or Riesz bases for L(R). In this paper we investigate the Balian–Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian–Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor S...
متن کاملDensity of Frames and Schauder Bases of Windowed Exponentials
This paper proves that every frame of windowed exponentials satisfies a Strong Homogeneous Approximation Property with respect to its canonical dual frame, and a Weak Homogeneous Approximation Property with respect to an arbitrary dual frame. As a consequence, a simple proof of the Nyquist density phenomenon satisfied by frames of windowed exponentials with one or finitely many generators is ob...
متن کاملOperator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
متن کامل