Doubly commuting submodules of the Hardy module over polydiscs

• Autorzy: Jaydeb Sarkar , Amol Sasane , Brett D. Wick
• Języki publikacji: EN

Abstrakty

EN

In this note we establish a vector-valued version of Beurling's theorem (the Lax-Halmos theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the "weak" completion problem in $H^{∞}(𝔻ⁿ)$.

Kategorie tematyczne

• 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones)
• 30H05: Bounded analytic functions
• 47A15: Invariant subspaces
• 46J15: Banach algebras of differentiable or analytic functions, H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 217
• Numer: 2
• Strony: 179-192

Daty

wydano

2013

Twórcy

autor

Jaydeb Sarkar

• Indian Statistical Institute, Statistics and Mathematics Unit, 8th Mile, Mysore Road, Bangalore, 560059, India

autor

Amol Sasane

• Mathematics Department, London School of Economics, Houghton Street, London WC2A 2AE, U.K.

autor

Brett D. Wick

• School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, U.S.A.

Identyfikatory

DOI

10.4064/sm217-2-5