Małgorzata Marta Czerwińska, and Anna Kamińska. "Complex rotundities and midpoint local uniform rotundity in symmetric spaces of measurable operators." Studia Mathematica 201.3 (2010): 253-285. <http://eudml.org/doc/285891>.
@article{MałgorzataMartaCzerwińska2010,
abstract = {We investigate the relationships between strongly extreme, complex extreme, and complex locally uniformly rotund points of the unit ball of a symmetric function space or a symmetric sequence space E, and of the unit ball of the space E(ℳ,τ) of τ-measurable operators associated to a semifinite von Neumann algebra (ℳ,τ) or of the unit ball in the unitary matrix space $C_\{E\}$. We prove that strongly extreme, complex extreme, and complex locally uniformly rotund points x of the unit ball of the symmetric space E(ℳ,τ) inherit these properties from their singular value function μ(x) in the unit ball of E with additional necessary requirements on x in the case of complex extreme points. We also obtain the full converse statements for the von Neumann algebra ℳ with a faithful, normal, σ-finite trace τ as well as for the unitary matrix space $C_\{E\}$. Consequently, corresponding results on the global properties such as midpoint local uniform rotundity, complex rotundity and complex local uniform rotundity follow.},
author = {Małgorzata Marta Czerwińska, Anna Kamińska},
journal = {Studia Mathematica},
keywords = {symmetric function space; symmetric sequence space; extreme points; midpoint local uniform rotundity; complex rotundity},
language = {eng},
number = {3},
pages = {253-285},
title = {Complex rotundities and midpoint local uniform rotundity in symmetric spaces of measurable operators},
url = {http://eudml.org/doc/285891},
volume = {201},
year = {2010},
}
TY - JOUR
AU - Małgorzata Marta Czerwińska
AU - Anna Kamińska
TI - Complex rotundities and midpoint local uniform rotundity in symmetric spaces of measurable operators
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 3
SP - 253
EP - 285
AB - We investigate the relationships between strongly extreme, complex extreme, and complex locally uniformly rotund points of the unit ball of a symmetric function space or a symmetric sequence space E, and of the unit ball of the space E(ℳ,τ) of τ-measurable operators associated to a semifinite von Neumann algebra (ℳ,τ) or of the unit ball in the unitary matrix space $C_{E}$. We prove that strongly extreme, complex extreme, and complex locally uniformly rotund points x of the unit ball of the symmetric space E(ℳ,τ) inherit these properties from their singular value function μ(x) in the unit ball of E with additional necessary requirements on x in the case of complex extreme points. We also obtain the full converse statements for the von Neumann algebra ℳ with a faithful, normal, σ-finite trace τ as well as for the unitary matrix space $C_{E}$. Consequently, corresponding results on the global properties such as midpoint local uniform rotundity, complex rotundity and complex local uniform rotundity follow.
LA - eng
KW - symmetric function space; symmetric sequence space; extreme points; midpoint local uniform rotundity; complex rotundity
UR - http://eudml.org/doc/285891
ER -
