|
A strongly diagonal power of algebraic order bounded disjointness preserving operators
Author(s):
Karim
Boulabiar;
Gerard
Buskes;
Gleb
Sirotkin
Journal:
Electron. Res. Announc. Amer. Math. Soc.
9
(2003),
94-98.
MSC (2000):
Primary 47B65, 06F20, 06F25
Posted:
October 8, 2003
Retrieve article in:
PDF
Abstract |
References |
Similar articles |
Additional information
Abstract:
An order bounded disjointness preserving operator  on an Archimedean vector lattice is algebraic if and only if the restriction of  to the vector sublattice generated by the range of  is strongly diagonal, where  is the degree of the minimal polynomial of  and  is its `valuation'.
References:
-
- 1.
- Yu. A. Abramovich, C. D. Aliprantis, An Invitation to Operator Theory, Graduate Studies Math., Vol. 50, Amer. Math. Soc., Providence, RI, 2002. MR 2003h:47072
- 2.
- Yu. A. Abramovich, A. K. Kitover, Inverses of disjointness preserving operators, Memoirs Amer. Math. Soc. 143 (2000), no. 679. MR 2000k:47047
- 3.
- C. D. Aliprantis, O. Burkinshaw, Positive Operators, Academic Press, Orlando, FL, 1985. MR 87h:47086
- 4.
- J. Araujo, E. Beckenstein, L. Narici, Biseparating maps and homeomorphic real-compactifications, J. Math. Ana. Appl. 12 (1995), 258-265. MR 96b:46038
- 5.
- W. Arendt, Spectral properties of Lamperti operators, Indiana Univ. Math. J. 32 (1983), 199-215. MR 85d:47040
- 6.
- W. Arendt, D. R. Hart, The spectrum of quasi-invertible disjointness preserving operators, J. Funct. Anal. 33 (1986), 149-167. MR 87j:47051
- 7.
- K. Boulabiar, G. Buskes, Polar decomposition of order bounded disjointness preserving operators, Proc. Amer. Math. Soc., To appear.
- 8.
- K. Boulabiar, G. Buskes, M. Henriksen, A generalization of a theorem on biseparating maps, J. Math. Ana. Appl. 280 (2003), 336-351.
- 9.
- J. J. Grobler, C. B. Huijsmans, Disjointness preserving operators on complex Riesz spaces, Positivity 1 (1997), 155-164. MR 99k:47079
- 10.
- K. Jarosz, Automatic continuity of separating linear isomorphisms, Bull. Canadian Math. Soc. 33 (1990), 139-144. MR 92j:46049
- 11.
- I. Kaplansky, Infinite Abelian Groups, University of Michigan Press, Ann Arbor, 1954. MR 16:444g
- 12.
- W. A. J. Luxemburg, B. de Pagter, A. R. Schep, Diagonals of the powers of an operator on a Banach lattice, Operator theory in function spaces and Banach lattices, Oper. Theory Adv. Appl., Vol. 75, Birkhäuser, 1995, pp. 223-273. MR 97i:47076
- 13.
- M. Meyer, Les homomorphismes d'espaces vectoriels réticulés complexes, C. R. Acad. Sci. Paris, Serie. I 292 (1981), 793-796. MR 82f:47051
- 14.
- P. Meyer-Nieberg, Banach Lattices, Springer-Verlag, Berlin, 1991. MR 93f:46025
Similar Articles:
Retrieve articles in Electronic Research Announcements
with MSC
(2000):
47B65, 06F20, 06F25
Retrieve articles in all Journals with MSC
(2000):
47B65, 06F20, 06F25
Additional Information:
Karim
Boulabiar
Affiliation:
IPEST, Université de Carthage, BP 51, 2070-La Marsa, Tunisia
Email:
karim.boulabiar@ipest.rnu.tn
Gerard
Buskes
Affiliation:
Department of Mathematics, University of Mississippi, MS 38677
Email:
mmbuskes@olemiss.edu
Gleb
Sirotkin
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115
Email:
sirotkin@math.niu.edu
DOI:
10.1090/S1079-6762-03-00116-1
PII:
S 1079-6762(03)00116-1
Keywords:
Algebraic,
disjointness preserving,
locally algebraic,
minimal polynomial,
orthomorphism,
strongly diagonal
Received by editor(s):
June 18, 2003
Posted:
October 8, 2003
Additional Notes:
The first and the second authors gratefully acknowledge support from the NATO Collaborative Linkage Grant \#PST.CLG.979398. The second author also acknowledges support from the Office of Naval Research Grant \#N00014-01-1-0322
Communicated by:
Svetlana Katok
Copyright of article:
Copyright
2003,
American Mathematical Society
|
Comments: webmaster@ams.org