## Coefficient multipliers on Banach spaces of analytic functions.(English)Zbl 1235.42004

Motivated by the paper of J. H. Wells [J. Lond. Math. Soc., II. Ser. 2, 549–556 (1970; Zbl 0198.18102)] they define the space $$Y\otimes Y$$, where $$X$$ and $$Y$$ are “homogeneous” Banach spaces of analytic functions on the unit disc $$\mathbb{D}$$, by the requirement that $$f$$ can be represented as $$f= \sum^\infty_{j=0} g_n* h_n$$, with $$g_n\in X$$, $$h_n\in Y$$ and $\sum^\infty_{n=1}\| g_n\|_X\| h_n\|_Y< \infty.$ The authors show that this construction is closely related to coefficient multipliers.

### MSC:

 42A45 Multipliers in one variable harmonic analysis 30A99 General properties of functions of one complex variable 46E15 Banach spaces of continuous, differentiable or analytic functions 46A45 Sequence spaces (including Köthe sequence spaces)

### Keywords:

Banach spaces; analytic functions; coefficient multipliers

Zbl 0198.18102
Full Text:

### References:

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