Mathematical Analysis
A Beurling type theorem in weighted Bergman spaces
Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 433-436.

For the vector-valued Hardy space H2(U) and the standard weighted Bergman space An(Y) with coefficient Hilbert spaces U and Y, we single out a class of contractive multipliers from H2(U) to An(Y) which we call partially isometric multipliers. We then show that a closed subspace MAn(Y) is invariant under the shift operator Sn:f(z)zf(z) if and only if M=ΦH2(U) for some partially isometric multiplier Φ from H2(U) to An(Y).

Soit H2(U) lʼespace de Hardy aux valeurs vectorielles et soit An(Y) lʼespace de Bergman aux valeurs vectorielles et au poids (1|z|2)n2, où les espaces des coefficients U et Y sont des espaces de Hilbert. Nous considérons une classe de multiplicateurs contractifs de H2(U) dans An(Y), que nous appelons multiplicateurs isométriques partiels. Nous montrons quʼun sous-espace MAn(Y) qui est invariant pour lʼoperateur Sn:f(z)zf(z) est inclus isometriquement dans An(Y) si et seulement si M=ΦH2(U) pour un multiplicateur isométrique partiel Φ de H2(U) dans An(Y).

Published online:
DOI: 10.1016/j.crma.2013.06.004
Ball, Joseph A. 1; Bolotnikov, Vladimir 2

1 Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA
2 Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
     author = {Ball, Joseph A. and Bolotnikov, Vladimir},
     title = {A {Beurling} type theorem in weighted {Bergman} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {433--436},
     publisher = {Elsevier},
     volume = {351},
     number = {11-12},
     year = {2013},
     doi = {10.1016/j.crma.2013.06.004},
     language = {en},
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Ball, Joseph A.; Bolotnikov, Vladimir. A Beurling type theorem in weighted Bergman spaces. Comptes Rendus. Mathématique, Volume 351 (2013) no. 11-12, pp. 433-436. doi : 10.1016/j.crma.2013.06.004.

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