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Approach regions for the square root of the Poisson kernel and boundary functions in certain Orlicz spaces

M. Brundin (2007)

Czechoslovak Mathematical Journal

If the Poisson integral of the unit disc is replaced by its square root, it is known that normalized Poisson integrals of L p and weak L p boundary functions converge along approach regions wider than the ordinary nontangential cones, as proved by Rönning and the author, respectively. In this paper we characterize the approach regions for boundary functions in two general classes of Orlicz spaces. The first of these classes contains spaces L Φ having the property L ∞ ⊂ L Φ ⊂ L p , 1 ≤ p < ∞ . The second contains spaces L Φ that...

Approximate amenability for Banach sequence algebras

H. G. Dales, R. J. Loy, Y. Zhang (2006)

Studia Mathematica

We consider when certain Banach sequence algebras A on the set ℕ are approximately amenable. Some general results are obtained, and we resolve the special cases where A = ℓ p for 1 ≤ p < ∞, showing that these algebras are not approximately amenable. The same result holds for the weighted algebras ℓ p ( ω ) .

Approximate and weak amenability of certain Banach algebras

P. Bharucha, R. J. Loy (2010)

Studia Mathematica

The notions of approximate amenability and weak amenability in Banach algebras are formally stronger than that of approximate weak amenability. We demonstrate an example confirming that approximate weak amenability is indeed actually weaker than either approximate or weak amenability themselves. As a consequence, we examine the (failure of) approximate amenability for ℓ p -sums of finite-dimensional normed algebras.

Approximate biflatness and Johnson pseudo-contractibility of some Banach algebras

Amir Sahami, Mohammad R. Omidi, Eghbal Ghaderi, Hamzeh Zangeneh (2020)

Commentationes Mathematicae Universitatis Carolinae

We study the structure of Lipschitz algebras under the notions of approximate biflatness and Johnson pseudo-contractibility. We show that for a compact metric space X , the Lipschitz algebras Lip α ( X ) and lip α ( X ) are approximately biflat if and only if X is finite, provided that 0 < α < 1 . We give a necessary and sufficient condition that a vector-valued Lipschitz algebras is Johnson pseudo-contractible. We also show that some triangular Banach algebras are not approximately biflat.

Approximate identities and Young type inequalities in Musielak-Orlicz spaces

Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura (2013)

Czechoslovak Mathematical Journal

We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces.

Approximate identities in Banach function algebras

H. G. Dales, A. Ülger (2015)

Studia Mathematica

In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractive Banach function algebra which is not equivalent to a uniform algebra....

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