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An operator algebraic proof of Agler's factorization theorem
Author(s):
Sneh
Lata;
Meghna
Mittal;
Vern
I.
Paulsen
Journal:
Proc. Amer. Math. Soc.
137
(2009),
3741-3748.
MSC (2000):
Primary 46L07;
Secondary 47L25
Posted:
May 27, 2009
MathSciNet review:
2529882
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Abstract:
We give a short direct proof of Agler's factorization theorem that uses the Blecher-Ruan-Sinclair characterization of operator algebras. The key ingredient of this proof is an operator algebra factorization theorem. Our proof provides some additional information about these factorizations in the case of polynomials.
References:
-
- 1.
- J. Agler, On the Representation of Certain Holomorphic Functions Defined on a Polydisk, Topics in Operator Theory: Ernst D. Hellinger Memorial Volume, Oper. Theory Adv. Appl., 48(1990), Birkhäuser, Basel, 47-66. MR 1207393 (93m:47013)
- 2.
- J. Agler and J. E. McCarthy, Pick Interpolation and Hilbert Function Spaces, Graduate Studies in Mathematics, 44, American Mathematical Society, Providence, RI, 2002. MR 1882259 (2003b:47001)
- 3.
- T. Ando, On a Pair of Commutative Contractions, Acta Sci. Math., 24(1963), 88-90. MR 0155193 (27:5132)
- 4.
- D. P. Blecher and V. I. Paulsen, Explicit Constructions of Universal Operator Algebras and Applications to Polynomial Factorization, Proc. Amer. Math. Soc., 112(1991), 839-850. MR 1049839 (91j:46093)
- 5.
- D. P. Blecher, Z. J. Ruan and A. M. Sinclair, A Characterization of Operator Algebras, J. Funct. Anal., 89(1990), 188-201. MR 1040962 (91b:47098)
- 6.
- B. Sz-Nagy, Sur les contractions de l'espace de Hilbert, Acta. Sci. Math., 15(1953), 87-92. MR 0058128 (15:326d)
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- J. von Neumann, Eine Spektraltheorie fur allgemeine Operatoren eines unitaren Raumes, Math. Nachr., 4(1951), 258-281. MR 0043386 (13:254a)
- 8.
- V. I. Paulsen, Completely Bounded Maps and Operator Algebras, Cambridge Studies in Advanced Mathematics, 78, Cambridge University Press, Cambridge, 2002. MR 1976867 (2004c:46118)
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Additional Information:
Sneh
Lata
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
snehlata@math.uh.edu
Meghna
Mittal
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
mittal@math.uh.edu
Vern
I.
Paulsen
Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email:
vern@math.uh.edu
DOI:
10.1090/S0002-9939-09-09928-6
PII:
S 0002-9939(09)09928-6
Received by editor(s):
July 9, 2008,
Received by editor(s) in revised form:
February 16, 2009
Posted:
May 27, 2009
Additional Notes:
This research was supported in part by NSF grant DMS-0600191.
Communicated by:
Marius Junge
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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