Reducible representations of abelian groups
- [1] Tel Aviv University, School of Mathematical Sciences, Tel Aviv 69978 (Israël)
Annales de l’institut Fourier (2001)
- Volume: 51, Issue: 5, page 1407-1418
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topAtzmon, Aharon. "Reducible representations of abelian groups." Annales de l’institut Fourier 51.5 (2001): 1407-1418. <http://eudml.org/doc/115952>.
@article{Atzmon2001,
abstract = {A criterion for reducibility of certain representations of abelian groups is established.
Among the applications of this criterion, we give a positive answer to the translation
invariant subspace problem for weighted $L^p$ spaces on locally compact abelian groups,
for even weights and $1<p<\infty $.},
affiliation = {Tel Aviv University, School of Mathematical Sciences, Tel Aviv 69978 (Israël)},
author = {Atzmon, Aharon},
journal = {Annales de l’institut Fourier},
keywords = {abelian groups; reducible representations; translation invariant subspaces; Abelian groups; translation; invariant subspaces},
language = {eng},
number = {5},
pages = {1407-1418},
publisher = {Association des Annales de l'Institut Fourier},
title = {Reducible representations of abelian groups},
url = {http://eudml.org/doc/115952},
volume = {51},
year = {2001},
}
TY - JOUR
AU - Atzmon, Aharon
TI - Reducible representations of abelian groups
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 5
SP - 1407
EP - 1418
AB - A criterion for reducibility of certain representations of abelian groups is established.
Among the applications of this criterion, we give a positive answer to the translation
invariant subspace problem for weighted $L^p$ spaces on locally compact abelian groups,
for even weights and $1<p<\infty $.
LA - eng
KW - abelian groups; reducible representations; translation invariant subspaces; Abelian groups; translation; invariant subspaces
UR - http://eudml.org/doc/115952
ER -
References
top- C. Apostol, Hyperinvariant subspaces for bilateral weighted shifts, Integral Equations and Operator Theory 7 (1984) Zbl0574.47005MR802365
- A. Atzmon, The existence of hyperinvariant subspaces, J. Operator Theory 11 (1984), 3-40 Zbl0583.47009MR739792
- A. Atzmon, An operator on a Fréchet space with no common invariant subspace with its inverse, J. Funct. Anal. 55 (1984), 68-77 Zbl0552.47006MR733034
- A. Atzmon, Irreducible representations of abelian groups, Proceedings, Harmonic Analysis 1359 (1987), 83-92, Springer-Verlag, Berlin Zbl0681.47017
- A. Atzmon, Entire functions, invariant subspaces and Fourier transforms, Israel Math. Conf. Proc. 11 (1997), 37-52 Zbl0907.30029
- A. Atzmon, M. Sodin, Completely indecomposable operators and a uniqueness theorem of Cartwright-Levinson type, J. Funct. Anal. 169 (1999), 164-188 Zbl0945.47012MR1726751
- A. Atzmon, M. Sodin, Addendum to the paper ``Completely indecomposable operators and a uniqueness theorem of Cartwright-Levinson type", J. Funct. Anal. 175 (2000), 248-249 Zbl0989.47010MR1774858
- A. Atzmon, The existence of translation invariant subspaces of symmetric self-adjoint sequence spaces on , J. Funct. Anal. 178 (2000), 372-380 Zbl0978.47022MR1802899
- J. Bracconier, L'analyse harmonique dans les groupes abélien, L'enseignement Mathématique II (1956) Zbl0070.02603
- B. Chevreau, C.M. Pearcy, A.L. Shields, Finitely connected domains G, representations of , and invariant subspaces, J. Operator Theory 6 (1981), 375-405 Zbl0525.47004MR643698
- R. Deville, G. Godefroy, V. Zizler, Smoothness and renorming in Banach spaces, 64 (1993), Longman, Harlow Zbl0782.46019
- Y. Domar, On the existence of nontrivial or nonstandard translation invariant subspaces of weighted and , 18th Scandinavian Congress of Mathematics (Aarhus, 1980) 11 (1981), 226-235 Zbl0468.47003
- Y. Domar, Translation invariant subspaces of weighted and spaces, Math. Scand. 49 (1981), 133-144 Zbl0443.47030MR645094
- Y. Domar, Translation invariant subspaces of weighted , Proceeding, Commutative Harmonic Analysis 91 (1987), A.M.S., Providence, R.I. Zbl0688.47002
- Y. Domar, Entire functions of order with bounds on both axes, Ann. Acad. Sci. Fenn. Math. 22 (1997), 339-348 Zbl0913.30017MR1469795
- J. Esterlé, Singular inner functions and biinvariant subspaces for disymmetric weighted shifts, J. Funct. Anal. 144 (1997), 61-104 Zbl0938.47003MR1430716
- J. Esterlé, A. Volberg, Sous-espaces invariant par translations bilatérales de certains espaces de Hilbert de suites quasianalytiquement pondérées, C.R. Acad. Sci. Paris, Série I 326 (1998), 295-300 Zbl0919.47009MR1648437
- J. Esterlé, A. Volberg, Analytic left-invariant subspaces of weighted Hilbert spaces of sequences Zbl1002.47001
- J. Esterlé, A. Volberg, Asymptotically holomorphic functions and translation invariant subspaces of weighted Hilbert spaces of sequences Zbl1059.47034
- R. Gellar, D. Herrero, Hyperinvariant subspaces of bilateral weighted shifts, Indiana Univ. Math. J. 23 (1974), 771-790 Zbl0253.46128MR331083
- G. Köthe, Topological vector spaces I, (1969), Springer-Verlag, New York Zbl0179.17001
- J. Lindenstrauss, On nonseparable reflexive Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 967-970 Zbl0156.36403MR205040
- C.J. Read, A solution to the invariant subspace problem in the space , Bull. London Math. Soc. 17 (1985), 305-317 Zbl0574.47006MR806634
- A.L. Shields, Weighted shift operators and analytic function theory, Topics in Operator Theory 13 (1974), AMS Math. Surveys, Providence, R.I. Zbl0303.47021
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.