87,124 research outputs found
A class of linear fractional maps of the ball and their composition operators
AbstractWe study a class of linear fractional self-maps of the ball which seems to be a good generalization of parabolic non-automorphisms of the unit disk. We give a normal form of these maps and use it to compute the spectrum of the composition operators induced by them. We also show that these composition operators are never hypercyclic. Applications are given to the study of more general linear fractional transformations
Pure state transformations induced by linear operators
We generalise Wigner's theorem to its most general form possible for B(h) in
the sense of completely characterising those vector state transformations of
B(h) that appear as restrictions of duals of linear operators on B(h). We then
use this result to similarly characterise the pure state transformations of
general C*-algebras that appear as restrictions of duals of linear operators on
the underlying algebras. This result may be interpreted as a noncommutative
Banach-Stone theorem.Comment: 24 pages, amslatex, revised and debugged versio
On the degree of Polar Transformations -- An approach through Logarithmic Foliations
We investigate the degree of the polar transformations associated to a
certain class of multi-valued homogeneous functions. In particular we prove
that the degree of the pre-image of generic linear spaces by a polar
transformation associated to a homogeneous polynomial is determined by the
zero locus of . For zero dimensional-dimensional linear spaces this was
conjecture by Dolgachev and proved by Dimca-Papadima using topological
arguments. Our methods are algebro-geometric and rely on the study of the Gauss
map of naturally associated logarithmic foliations
Extremal varieties 3-rationally connected by cubics, quadro-quadric Cremona transformations and rank 3 Jordan algebras
For any , we prove that there exist equivalences between these
apparently unrelated objects: irreducible -dimensional non degenerate
projective varieties different from rational normal
scrolls and 3-covered by twisted cubic curves, up to projective equivalence;
quadro-quadric Cremona transformations of , up to linear
equivalence; -dimensional complex Jordan algebras of rank three, up to
isotopy.
We also provide some applications to the classification of particular classes
of varieties in the class defined above and of quadro-quadric Cremona
transformations, proving also a structure theorem for these birational maps and
for varieties 3-covered by twisted cubics by reinterpreting for these objects
the solvability of the radical of a Jordan algebra.Comment: 30 pages, 1 figure. Corrected typo
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