Contents/conteúdo

Mathematics Department Técnico Técnico

Operator Theory, Complex Analysis and Applications Seminar  RSS

Sessions

11/11/2014, 16:30 — 17:30 — Room P4.35, Mathematics Building
, University of Agriculture in Krakow

Invitation to weighted shifts on directed trees

Weighted shifts on directed trees form an important class of operators introduced recently in [6]. This class is a natural and substantial generalization of the class of classical (unilateral or bilateral) weighted shifts on $\ell^2$ spaces. It is also related to a class of composition operators in $L^2$-spaces.

Weighted shifts on directed trees have proven to have very interesting features (see [2, 3, 5, 6, 7]). The underlying relatively simple graph structure gives a rise to a subtle and complex structure of the operators, which turn out to have properties not known before in other classes of operators, and makes them ideal for testing hypothesises and constructing examples. We will outline recent results concerning these operators with main emphasis on on subnormality and reflexivity.

The talk is based on a joint work with Z.J. Jabloński, I.B. Jung and J. Stochel, and M. Ptak.

References

  1. P. Budzyński, P. Dymek, Z. J. Jabłoski, J. Stochel, Subnormal weighted shifts on directed trees and composition operators in $L^2$-spaces with non-densely defined powers, Abstract Appl. Anal. (2014), Article ID 791817, 6 pages.
  2. P. Budzyński, Z. J. Jabłoski, I. B. Jung, J. Stochel, Subnormality of unbounded weighted shifts on directed trees, J. Math. Anal. Appl. 394 (2012), 819-834.
  3. P. Budzyński, Z. J. Jabłoski, I. B. Jung, J. Stochel, Subnormality of unbounded weighted shifts on directed trees. II, J. Math. Anal. Appl. 398 (2013), 600-608.
  4. P. Budzyński, Z. J. Jabłoski, I. B. Jung, J. Stochel, Unbounded subnormal composition operators in $L^2$-spaces, preprint, http://arxiv.org/abs/1310.3542.
  5. P. Budzyński, Z. J. Jabłoski, I. B. Jung, J. Stochel, Subnormal weighted shifts on directed trees whose nth powers have trivial domain, preprint, http://arxiv.org/abs/1409.8022.
  6. Z. J. Jabłoński, I. B. Jung, J. Stochel, Weighted shifts on directed trees, Mem. Amer. Math. Soc 216 (2012), no. 1017.
  7. Z. J. Jabłoński, I. B. Jung, J. Stochel, A non-hyponormal operator generating Stieltjes moment sequences, J. Funct. Anal. 262 (2012), 3946-3980.

Seminar organized in the context of the project PTDC/MAT/121837/2010.

CAMGSDCMAT - U MinhoFCT