Page 208 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 208
RECENT DEVELOPMENTS ON PRESERVERS (MS-38)
where σ : H → F, |σ(x)| = 1, x ∈ H, is a so called phase function. In this talk several
generalizations of this theorem to the setting of normed spaces will be presented.
Meet preservers between lattices of real-valued continuous functions
Kristopher Lee, leekm@iastate.edu
Iowa State University, United States
It is well-know that the set C(X) of real-valued continuous functions defined on a compact
Hausdorff space X becomes a lattice when equipped with the usual point-wise ordering; in
particular, the join and meet of f, g ∈ C(X) are given by
(f ∨ g)(x) = max{f (x), g(x)} and (f ∧ g)(x) = min{f (x), g(x)},
respectively. We will demonstrate that any surjective T : C(X) → C(Y ) satisfying
Ranπ(f ∧ g) = Ranπ(T (f ) ∧ T (g))
for all f, g ∈ C(X), where Ranπ(·) denotes the set of range values of maximum absolute value,
induces a homeomorphism ψ : Y → X such that
T (f ) = f ◦ ψ
holds for all f ∈ C(X) with 0 ≤ f .
On the linearity of order-isomorphisms
Bas Lemmens, b.lemmens@kent.ac.uk
University of Kent, United Kingdom
A basic problem in the theory of partially ordered vector spaces is to understand when order-
isomorphisms are affine. This depends in a subtle way on the geometry of the cones involved.
In this talk I will discuss some recent progress on this problem, mainly based on joint with van
Gaans and van Imhoff. We will introduce a new condition on the extreme rays of the cone,
which ensures that all order-isomorphisms are affine. The condition is milder than existing
ones and is satisfied by, for example, the cone of positive operators in the space of bounded
self-adjoint operators on a Hilbert space.
Unitarily Invariant Norms on Operators and Distance Preserving Maps
Chi Kwong Li, ckli@math.wm.edu
College of William and Mary, United States
We discuss some inequalities related to some classes of unitarily invariant norms on the set of
bounded linear operators between two Hilbert spaces, and the characterization of the distance
preserving maps for such norms.
206
where σ : H → F, |σ(x)| = 1, x ∈ H, is a so called phase function. In this talk several
generalizations of this theorem to the setting of normed spaces will be presented.
Meet preservers between lattices of real-valued continuous functions
Kristopher Lee, leekm@iastate.edu
Iowa State University, United States
It is well-know that the set C(X) of real-valued continuous functions defined on a compact
Hausdorff space X becomes a lattice when equipped with the usual point-wise ordering; in
particular, the join and meet of f, g ∈ C(X) are given by
(f ∨ g)(x) = max{f (x), g(x)} and (f ∧ g)(x) = min{f (x), g(x)},
respectively. We will demonstrate that any surjective T : C(X) → C(Y ) satisfying
Ranπ(f ∧ g) = Ranπ(T (f ) ∧ T (g))
for all f, g ∈ C(X), where Ranπ(·) denotes the set of range values of maximum absolute value,
induces a homeomorphism ψ : Y → X such that
T (f ) = f ◦ ψ
holds for all f ∈ C(X) with 0 ≤ f .
On the linearity of order-isomorphisms
Bas Lemmens, b.lemmens@kent.ac.uk
University of Kent, United Kingdom
A basic problem in the theory of partially ordered vector spaces is to understand when order-
isomorphisms are affine. This depends in a subtle way on the geometry of the cones involved.
In this talk I will discuss some recent progress on this problem, mainly based on joint with van
Gaans and van Imhoff. We will introduce a new condition on the extreme rays of the cone,
which ensures that all order-isomorphisms are affine. The condition is milder than existing
ones and is satisfied by, for example, the cone of positive operators in the space of bounded
self-adjoint operators on a Hilbert space.
Unitarily Invariant Norms on Operators and Distance Preserving Maps
Chi Kwong Li, ckli@math.wm.edu
College of William and Mary, United States
We discuss some inequalities related to some classes of unitarily invariant norms on the set of
bounded linear operators between two Hilbert spaces, and the characterization of the distance
preserving maps for such norms.
206
