Normability of Lorentz spaces—an alternative approach

Gogatishvili, Amiran, and Soudský, Filip. "Normability of Lorentz spaces—an alternative approach." Czechoslovak Mathematical Journal 64.3 (2014): 581-597. <http://eudml.org/doc/262183>.

@article{Gogatishvili2014,
abstract = {We study normability properties of classical Lorentz spaces. Given a certain general lattice-like structure, we first prove a general sufficient condition for its associate space to be a Banach function space. We use this result to develop an alternative approach to Sawyer’s characterization of normability of a classical Lorentz space of type $\Lambda $. Furthermore, we also use this method in the weak case and characterize normability of $\Lambda _\{v\}^\{\infty \}$. Finally, we characterize the linearity of the space $\Lambda _\{v\}^\{\infty \}$ by a simple condition on the weight $v$.},
author = {Gogatishvili, Amiran, Soudský, Filip},
journal = {Czechoslovak Mathematical Journal},
keywords = {weighted Lorentz space; weighted inequality; non-increasing rearrangement; Banach function space; associate space; weighted Lorentz space; weighted inequality; non-increasing rearrangement; Banach function space; associate space},
language = {eng},
number = {3},
pages = {581-597},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Normability of Lorentz spaces—an alternative approach},
url = {http://eudml.org/doc/262183},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Gogatishvili, Amiran
AU - Soudský, Filip
TI - Normability of Lorentz spaces—an alternative approach
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 581
EP - 597
AB - We study normability properties of classical Lorentz spaces. Given a certain general lattice-like structure, we first prove a general sufficient condition for its associate space to be a Banach function space. We use this result to develop an alternative approach to Sawyer’s characterization of normability of a classical Lorentz space of type $\Lambda $. Furthermore, we also use this method in the weak case and characterize normability of $\Lambda _{v}^{\infty }$. Finally, we characterize the linearity of the space $\Lambda _{v}^{\infty }$ by a simple condition on the weight $v$.
LA - eng
KW - weighted Lorentz space; weighted inequality; non-increasing rearrangement; Banach function space; associate space; weighted Lorentz space; weighted inequality; non-increasing rearrangement; Banach function space; associate space
UR - http://eudml.org/doc/262183
ER -