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w * -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

We observe that a separable Banach space X is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if ℒ ( X , Y ) is not reflexive for reflexive X and Y then ℒ ( X 1 , Y ) is is not reflexive for some X 1 ⊂ X , X 1 having a basis.

Wavelet bases in L p ( ℝ )

Gustaf Gripenberg (1993)

Studia Mathematica

It is shown that an orthonormal wavelet basis for L 2 ( ℝ ) associated with a multiresolution is an unconditional basis for L p ( ℝ ) , 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.

Wavelet frames for distributions; local and pointwise regularity

Hans Triebel (2003)

Studia Mathematica

This paper deals with wavelet frames for a large class of distributions on euclidean n-space, including all compactly supported distributions. These representations characterize the global, local, and pointwise regularity of the distribution considered.

Wavelet techniques for pointwise regularity

Stéphane Jaffard (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Let E be a Banach (or quasi-Banach) space which is shift and scaling invariant (typically a homogeneous Besov or Sobolev space). We introduce a general definition of pointwise regularity associated with E , and denoted by C E α ( x 0 ) . We show how properties of E are transferred into properties of C E α ( x 0 ) . Applications are given in multifractal analysis.

Wavelet transform for functions with values in UMD spaces

Cornelia Kaiser, Lutz Weis (2008)

Studia Mathematica

We extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces. As a by-product we obtain equivalent norms on Bochner spaces in terms of g-functions.

Weak amenability of the second dual of a Banach algebra

M. Eshaghi Gordji, M. Filali (2007)

Studia Mathematica

It is known that a Banach algebra inherits amenability from its second Banach dual **. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this class of...

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