We study the geometric and approximation properties of Marcinkiewicz spaces and Stepanoff spaces, $1 \leq p < \infty$, as well as others where translations are not isometric but bounded (the bounded $p$-mean spaces) or even unbounded ($\Mean0$). We construct a function $f$ that belongs to these spaces and has the unusual and unexpected property that all approximate identities $\phi_\varepsilon*f$ converge to $f$ pointwise but they never converge in norm.

Andreano, F., & Picardello, A.M. (2009). Approximate identities on some homogeneous Banach spaces. MONATSHEFTE FÜR MATHEMATIK, 158, 235-246 [10.1007/s00605-009-0106-2].

### Approximate identities on some homogeneous Banach spaces

#### Abstract

We study the geometric and approximation properties of Marcinkiewicz spaces and Stepanoff spaces, $1 \leq p < \infty$, as well as others where translations are not isometric but bounded (the bounded $p$-mean spaces) or even unbounded ($\Mean0$). We construct a function $f$ that belongs to these spaces and has the unusual and unexpected property that all approximate identities $\phi_\varepsilon*f$ converge to $f$ pointwise but they never converge in norm.
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Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/03 - Geometria
eng
Marcinkiewicz spaces, Stepanoff spaces, bounded-p-means, approximate identities, bounded translations
Andreano, F., & Picardello, A.M. (2009). Approximate identities on some homogeneous Banach spaces. MONATSHEFTE FÜR MATHEMATIK, 158, 235-246 [10.1007/s00605-009-0106-2].
Andreano, F; Picardello, Am
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/28790
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