Let $T\colon L^p({\mathcal M})\to N})$ be a bounded operator between two noncommutative $L^p$-spaces, $1\leq p<\infty$. We say that $T$ is $\ell^1$-bounded (resp. $\ell^1$-contractive) if $T\otimes I_{\ell^1}$ extends to contractive) map from $L^p({\mathcal M};\ell^1)$ into N};\ell^1)$. show Yeadon's factorization theorem for $L^p$-isometries, p\not=2 <\infty$, applies an isometry L^2({\mathcal...

Let ? be a weight function defined on locally compact group G, 1?p<+?, S?G and let us assume that for any s?S, the left translation operator Ts is continuous from weighted Lp-space Lp(G,?) into itself. For given set ??C, vector f?Lp(G,?) said to (?,S)-dense if {?Tsf:???,s?S} dense in Lp(G,?). In this paper, we characterize existence of vectors terms ?.

Let we have a weighted Hardy-type integral operator T : Lp(a, b)→ Lp(a, b), −∞ ≤ a < b ≤ ∞, which is defined by (Tf) (x) = v(x) x ∫

The purpose of this paper is to establish Lp error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates Lp Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the Lp norm of the functi...

The purpose of this paper is to establish Lp error estimates, a Bernstein inequality, and inverse theorems for approximation by a space comprising spherical basis functions located at scattered sites on the unit n-sphere. In particular, the Bernstein inequality estimates Lp Bessel-potential Sobolev norms of functions in this space in terms of the minimal separation and the Lp norm of the functi...