Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

An operator algebraic proof of Agler's factorization theorem


Authors: Sneh Lata, Meghna Mittal and Vern I. Paulsen
Journal: Proc. Amer. Math. Soc. 137 (2009), 3741-3748
MSC (2000): Primary 46L07; Secondary 47L25
DOI: https://doi.org/10.1090/S0002-9939-09-09928-6
Published electronically: May 27, 2009
MathSciNet review: 2529882
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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)
  • 7. 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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46L07, 47L25

Retrieve articles in all journals with MSC (2000): 46L07, 47L25


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: https://doi.org/10.1090/S0002-9939-09-09928-6
Received by editor(s): July 9, 2008
Received by editor(s) in revised form: February 16, 2009
Published electronically: May 27, 2009
Additional Notes: This research was supported in part by NSF grant DMS-0600191.
Communicated by: Marius Junge
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society