Page 206 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 206
RECENT DEVELOPMENTS ON PRESERVERS (MS-38)
On maps preserving products equal to fixed elements
Louisa Catalano, catalanl@union.edu
Union College, United States
Coauthor: Hayden Julius
In this talk, we will characterize the form of bijective linear maps f : Mn(C) → Mn(C)
satisfying f (A)f (B) = M whenever AB = N , where M and N are fixed n × n complex
matrices.
Total variation distance isometries of probability measures
Gregor Dolinar, gregor.dolinar@fe.uni-lj.si
University of Ljubljana, Slovenia
Coauthors: Bojan Kuzma, Djordje Mitrovic´
Some recent results about surjective isometries of Borel probability measures with respect to
the total variation distance will be presented. It turns out that the characterization of such
isometries under some additional assumption, e.g. w*-continuity or absolute continuity with
respect to some fixed probability measure is quite different than in the general case of surjective
isometries on all probability measures.
The minimax principle in the Jordan setting
Francisco J. Fernandez Polo, pacopolo@ugr.es
University of Granada, Spain
The celebrated minimax principle (also known as Courant-Fisher Minimax theorem) provides a
characterization of the eigenvalues of a symmetric compact operator on a Hilbert space without
any reference to eigenvectors or the characteristic polynomial.
In the Jordan setting it is remarkable the contribution of U. Hirzebruch, who obtained in
1970 a minimax principle for finite dimensional formally real Jordan algebras (finite dimen-
sional JB-algebras).
We present a generalized minimax principle for weakly compact JB∗-triples (and hence also
for weakly compact JB∗-algebras). This result provides a geometric characterization of the
singular values associated to an element. As consequences of this principle a Weyl inequality
and a Cauchy-Poincaré interlacing Theorem can also be obtained.
204
On maps preserving products equal to fixed elements
Louisa Catalano, catalanl@union.edu
Union College, United States
Coauthor: Hayden Julius
In this talk, we will characterize the form of bijective linear maps f : Mn(C) → Mn(C)
satisfying f (A)f (B) = M whenever AB = N , where M and N are fixed n × n complex
matrices.
Total variation distance isometries of probability measures
Gregor Dolinar, gregor.dolinar@fe.uni-lj.si
University of Ljubljana, Slovenia
Coauthors: Bojan Kuzma, Djordje Mitrovic´
Some recent results about surjective isometries of Borel probability measures with respect to
the total variation distance will be presented. It turns out that the characterization of such
isometries under some additional assumption, e.g. w*-continuity or absolute continuity with
respect to some fixed probability measure is quite different than in the general case of surjective
isometries on all probability measures.
The minimax principle in the Jordan setting
Francisco J. Fernandez Polo, pacopolo@ugr.es
University of Granada, Spain
The celebrated minimax principle (also known as Courant-Fisher Minimax theorem) provides a
characterization of the eigenvalues of a symmetric compact operator on a Hilbert space without
any reference to eigenvectors or the characteristic polynomial.
In the Jordan setting it is remarkable the contribution of U. Hirzebruch, who obtained in
1970 a minimax principle for finite dimensional formally real Jordan algebras (finite dimen-
sional JB-algebras).
We present a generalized minimax principle for weakly compact JB∗-triples (and hence also
for weakly compact JB∗-algebras). This result provides a geometric characterization of the
singular values associated to an element. As consequences of this principle a Weyl inequality
and a Cauchy-Poincaré interlacing Theorem can also be obtained.
204
