Continuous isometric semigroups and reflexivity
Marek Ptak
Annales Polonici Mathematici, Tome 55 (1991), p. 21-28 / Harvested from The Polish Digital Mathematics Library

 Abstract. We consider the reflexivity of a WOT-closed algebra generated by continuous isometric semigroups parametrized by the semigroup of non-negative reals or the semigroup of finite sequences of non-negative reals. It is also proved that semigroups of continuous unilateral multi-parameter shifts are reflexive.

Publié le : 1991-01-01
EUDML-ID : urn:eudml:doc:264257
@article{bwmeta1.element.desklight-4293e18c-34dc-45f5-b310-96f199715330,
     author = {Marek Ptak},
     title = {Continuous isometric semigroups and reflexivity},
     journal = {Annales Polonici Mathematici},
     volume = {55},
     year = {1991},
     pages = {21-28},
     zbl = {0767.47021},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.desklight-4293e18c-34dc-45f5-b310-96f199715330}
}
Marek Ptak. Continuous isometric semigroups and reflexivity. Annales Polonici Mathematici, Tome 55 (1991) pp. 21-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.desklight-4293e18c-34dc-45f5-b310-96f199715330/

[00000] [1] J. A. Deddens, Every isometry is reflexive. Proc. Amer, Math. Soc. 28 (1971), 509-511. | Zbl 0213.14304

[00001] [2] D. Gaşpar and N. Suciu, On the structure of isometric semigroups, in: Oper. Theory: Adv. Appl. 14, Birkhauser, Basel 1984, 125-139.

[00002] [3] M. Ptak, On the reflexivity of pairs of isometries and of tensor products of some operator algebras. Studia Math. 83 (1986), 47-55. | Zbl 0549.47012

[00003] [4] M. Ptak, Reflexivity of multiplication operators on certain domains in CN, Bull. Polish Acad, Sci. Math. 37 (1989), 217-220. | Zbl 0771.47017

[00004] [5] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990), 409 -415. | Zbl 0734.47023

[00005] [6] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, New York 1973. | Zbl 0269.47003

[00006] [7] M. Słociński, On the Wold-type decomposition of a pair of commuting Isometries, Ann. Polon. Math. 37 (1980), 255-262. | Zbl 0485.47018

[00007] [8] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam 1974. | Zbl 0201.45003