TY - JOUR
T1 - Geometry of unit balls of free Banach lattices, and its applications
AU - Oikhberg, T.
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/4/15
Y1 - 2024/4/15
N2 - We begin by describing the unit ball of the free p-convex Banach lattice over a Banach space E (denoted by FBL(p)[E]) as a closed solid convex hull of an appropriate set. Based on it, we show that, if a Banach space E has the λ-Approximation Property, then FBL(p)[E] has the λ-Positive Approximation Property. Further, we show that operators u∈B(E,F) (where E and F are Banach spaces) which extend to lattice homomorphisms from FBL(q)[E] to FBL(p)[F] are precisely those whose adjoints are (q,p)-mixing. Related results are also obtained for free lattices with an upper p-estimate.
AB - We begin by describing the unit ball of the free p-convex Banach lattice over a Banach space E (denoted by FBL(p)[E]) as a closed solid convex hull of an appropriate set. Based on it, we show that, if a Banach space E has the λ-Approximation Property, then FBL(p)[E] has the λ-Positive Approximation Property. Further, we show that operators u∈B(E,F) (where E and F are Banach spaces) which extend to lattice homomorphisms from FBL(q)[E] to FBL(p)[F] are precisely those whose adjoints are (q,p)-mixing. Related results are also obtained for free lattices with an upper p-estimate.
KW - Approximation property
KW - Free Banach lattice
KW - Mixing operator
KW - p-summing operator
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U2 - 10.1016/j.jfa.2024.110351
DO - 10.1016/j.jfa.2024.110351
M3 - Article
AN - SCOPUS:85184602034
SN - 0022-1236
VL - 286
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
M1 - 110351
ER -