On commuting operators solving Gleason’s problem
HTML articles powered by AMS MathViewer
- by D. Alpay and C. Dubi PDF
- Proc. Amer. Math. Soc. 133 (2005), 3285-3293 Request permission
Abstract:
We prove the uniqueness of commuting operators solving Gleason’s problem for certain spaces of functions analytic in the unit ball.References
- Daniel Alpay, The Schur algorithm, reproducing kernel spaces and system theory, SMF/AMS Texts and Monographs, vol. 5, American Mathematical Society, Providence, RI; Société Mathématique de France, Paris, 2001. Translated from the 1998 French original by Stephen S. Wilson. MR 1839648
- D. Alpay and C. Dubi, Backward shift operator and finite dimensional de Branges Rovnyak spaces in the ball, Linear Algebra Appl. 371 (2003), 277–285. MR 1997376, DOI 10.1016/S0024-3795(03)00456-7
- Daniel Alpay and H. Turgay Kaptanoğlu, Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem, Integral Equations Operator Theory 42 (2002), no. 1, 1–21. MR 1866874, DOI 10.1007/BF01203020
- Daniel Alpay and H. Turgay Kaptanoğlu, Gleason’s problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball, J. Math. Anal. Appl. 276 (2002), no. 2, 654–672. MR 1944782, DOI 10.1016/S0022-247X(02)00412-2
- Evgueni Doubtsov, Minimal solutions of the Gleason problem, Complex Variables Theory Appl. 36 (1998), no. 1, 27–35. MR 1637332, DOI 10.1080/17476939808815097
- Evgueni Doubtsov, Leibenzon’s backward shift and composition operators, Proc. Amer. Math. Soc. 129 (2001), no. 12, 3495–3499. MR 1860481, DOI 10.1090/S0002-9939-01-06325-0
- Harry Dym, $J$ contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, CBMS Regional Conference Series in Mathematics, vol. 71, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1989. MR 1004239, DOI 10.1090/cbms/071
- Andrew M. Gleason, Finitely generated ideals in Banach algebras, J. Math. Mech. 13 (1964), 125–132. MR 0159241
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594, DOI 10.1007/978-1-4613-8098-6
- Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083
Additional Information
- D. Alpay
- Affiliation: Department of Mathematics, Ben–Gurion University of the Negev, Beer-Sheva 84105, Israel
- MR Author ID: 223612
- Email: dany@math.bgu.ac.il
- C. Dubi
- Affiliation: Department of Mathematics, Ben–Gurion University of the Negev, Beer-Sheva 84105, Israel
- Address at time of publication: Department of Mathematics, Weizmann Institute, POB 26, Rehovot 76100, Israel
- Email: dubi@math.bgu.ac.il, dubic@weizmann.ac.il
- Received by editor(s): February 3, 2004
- Received by editor(s) in revised form: June 12, 2004
- Published electronically: May 2, 2005
- Communicated by: Joseph A. Ball
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 3285-3293
- MSC (2000): Primary 47B32
- DOI: https://doi.org/10.1090/S0002-9939-05-07839-1
- MathSciNet review: 2161151