Annales Academiæ Scientiarum Fennicæ Mathematica

Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 1045-1061

Alessandro Monguzzi and Giulia Sarfatti

Università degli Studi di Milano, Dipartimento di Matematica
Via C. Saldini 50, 20133 Milano, Italy; alessandro.monguzzi 'at' unimi.it

Università di Firenze, Dipartimento di Matematica e Informatica "U. Dini"
Viale Morgagni 67/A, 50134 Firenze, Italy; giulia.sarfatti 'at' unifi.it

Abstract. In this paper we characterize the closed invariant subspaces for the (*-)multiplier operator of the quaternionic space of slice L² functions. As a consequence, we obtain the inner-outer factorization theorem for the quaternionic Hardy space on the unit ball and we provide a characterization of quaternionic outer functions in terms of cyclicity.

2010 Mathematics Subject Classification: Primary 30G35, 30H10, 30J05.

Key words: Functions of a quaternionic variable, invariant subspaces, inner-outer factorization.

Reference to this article: A. Monguzzi and G. Sarfatti: Shift invariant subspaces of slice L² functions. Ann. Acad. Sci. Fenn. Math. 43 (2018), 1045-1061.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4366