Continuous isometric semigroups and reflexivity

Marek Ptak

Annales Polonici Mathematici (1991)

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

Abstract

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 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.

How to cite

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Marek 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

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  1. [1] J. A. Deddens, Every isometry is reflexive. Proc. Amer, Math. Soc. 28 (1971), 509-511. Zbl0213.14304
  2. [2] D. Gaşpar and N. Suciu, On the structure of isometric semigroups, in: Oper. Theory: Adv. Appl. 14, Birkhauser, Basel 1984, 125-139. 
  3. [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. [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. [5] M. Ptak, Reflexivity of pairs of shifts, Proc. Amer. Math. Soc. 109 (1990), 409 -415. Zbl0734.47023
  6. [6] H. Radjavi and P. Rosenthal, Invariant Subspaces, Springer, New York 1973. Zbl0269.47003
  7. [7] M. Słociński, On the Wold-type decomposition of a pair of commuting Isometries, Ann. Polon. Math. 37 (1980), 255-262. Zbl0485.47018
  8. [8] B. Sz.-Nagy and C. Foiaş, Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam 1974. Zbl0201.45003

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