# Continuous isometric semigroups and reflexivity

Annales Polonici Mathematici (1991)

- Volume: 54, Issue: 1, page 21-28
- ISSN: 0066-2216

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topMarek Ptak. "Continuous isometric semigroups and reflexivity." Annales Polonici Mathematici 54.1 (1991): 21-28. <http://eudml.org/doc/264257>.

@article{MarekPtak1991,

abstract = { 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.},

author = {Marek Ptak},

journal = {Annales Polonici Mathematici},

keywords = {reflexivity of a WOT-closed algebra generated by continuous isometric semigroups; semigroup of non-negative reals; semigroup of finite sequences of non-negative reals; semigroups of continuous unilateral multi- parameter shifts are reflexive},

language = {eng},

number = {1},

pages = {21-28},

title = {Continuous isometric semigroups and reflexivity},

url = {http://eudml.org/doc/264257},

volume = {54},

year = {1991},

}

TY - JOUR

AU - Marek Ptak

TI - Continuous isometric semigroups and reflexivity

JO - Annales Polonici Mathematici

PY - 1991

VL - 54

IS - 1

SP - 21

EP - 28

AB - 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.

LA - eng

KW - reflexivity of a WOT-closed algebra generated by continuous isometric semigroups; semigroup of non-negative reals; semigroup of finite sequences of non-negative reals; semigroups of continuous unilateral multi- parameter shifts are reflexive

UR - http://eudml.org/doc/264257

ER -

## References

top- [1] J. A. Deddens, Every isometry is reflexive. Proc. Amer, Math. Soc. 28 (1971), 509-511. Zbl0213.14304
- [2] D. Gaşpar and N. Suciu, On the structure of isometric semigroups, in: Oper. Theory: Adv. Appl. 14, Birkhauser, Basel 1984, 125-139.
- [3] M. Ptak, On the reflexivity of pairs of isometries and of tensor products of some operator algebras. Studia Math. 83 (1986), 47-55. Zbl0549.47012
- [4] M. Ptak, Reflexivity of multiplication operators on certain domains in ${C}^{N}$, Bull. Polish Acad, Sci. Math. 37 (1989), 217-220. Zbl0771.47017
- [5] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990), 409 -415. Zbl0734.47023
- [6] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, New York 1973. Zbl0269.47003
- [7] M. Słociński, On the Wold-type decomposition of a pair of commuting Isometries, Ann. Polon. Math. 37 (1980), 255-262. Zbl0485.47018
- [8] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam 1974. Zbl0201.45003

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