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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
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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, 1, 107-110 (1995) · Zbl 0821.47022 · doi:10.1155/S0161171295000147
[2] Shields, A. L., Weighted shift operators and analytic function theory, Math. Survey, A.M.S. Providenc, 13, 49-128 (1974) · Zbl 0303.47021
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