## On the space $$\ell^p(\beta)$$.(English)Zbl 0952.47027

Given a sequence $$(\beta_n)_n$$ of positive weights, the author studies the Banach space $$\ell^p(\beta)$$ of all power series $$f(z)= \sum^\infty_{n=0} \widehat f(n)z^n$$ for which the norm $\|f\|:= \Biggl(\sum^\infty_{n= 0}|\widehat f(n)|^p \beta^p_n\Biggr)^{1/p}$ makes sense and is finite.

### MSC:

 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) 46B45 Banach sequence spaces 47A25 Spectral sets of linear operators

### Keywords:

power series space; positive weights
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### References:

 [1] Seddighi K., Hedayatiyan K., Yousefi B.,Operators acting on certain Banach spaces of analytic functions, International Journal of Mathematics and Mathemathical Sciences,18, n. 1 (1995), 107–110. · Zbl 0821.47022 [2] Shields A.L.,Weighted shift operators and analytic function theory, Math. Survey, A.M.S. Providenc,13 (1974), 49–128. · Zbl 0303.47021
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