On Orlicz sequence algebras

Abstract

Abstract We study Orlicz sequence algebras and their properties. In particular, we fully characterize biflat and biprojective Orlicz sequence algebras as well as weakly amenable and approximately (semi-)amenable Orlicz sequence algebras. As a consequence, we show the existence of a wide class of sequence algebras that behave differently—in terms of the amenability properties—from any of the algebras ℓ p , 1 ⩽ p ⩽ ∞ $\ell _{p}, 1\leqslant p\leqslant \infty $ .

Keywords

• Orlicz function
• Orlicz sequence space/algebra
• Arens regularity
• Character space
• Biprojective/biflat algebra
• (Weakly) amenable algebra