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Abstract. The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces H K on the unit ball in C n , wandering subspaces for restrictions of the multiplication tuple M z = (M z1 , . . . , M zn ) can be described in terms of suitable H K -inner functions. We prove that H K -inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogenous polynomials as an application. Along the way we prove a refinement of a result of Arveson on the uniqueness of minimal dilations of pure row contractions.

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In this article, we study a class of contractive factors of\break m-hypercontractions for m∈N. We find a characterization of such factors and it is achieved by finding explicit dilations of these factors on certain weighted Bergman spaces. This is a generalization of the work done by {B.K. Das, S. Sarkar, J. Sarkar}, Factorization of contraction, \textit{Adv. in Math.} \textbf{322}(2017), 186--200.

In this article, we study a class of contractive factors of m-hypercontractions for m ∈ N. We find a characterization of such factors and this is achieved by finding explicit dilation of these factors on some weighted Bergman spaces. This is a generalization of the work done in [14].

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