Bishop, Christopher J. An indestructible Blaschke product in the little Bloch space. (English) Zbl 0810.30024 Publ. Mat., Barc. 37, No. 1, 95-109 (1993). An infinite Blaschke product \(B\) is constructed so that \(B(z)- a/(1- \bar a B(z))\) is in the little Bloch space \({\mathcal B}_ 0\) for all complex \(a\), \(| a|< 1\). This answers in the affirmative a question posed by K. Stephenson. Also, a VMOA function \(f: \| f\|_{H^ \infty}= 1\) is constructed whose range set \(R(f,a):= \{w: \exists z_ n\to a,\;f(z_ n)= w\}\) at each point \(a\) on the unit circle equals the whole open unit disk. Reviewer: D.Khavinson (Fayetteville) Cited in 6 Documents MSC: 30D45 Normal functions of one complex variable, normal families 30D50 Blaschke products, etc. (MSC2000) Keywords:Bloch space; Blaschke product; little Bloch space PDFBibTeX XMLCite \textit{C. J. Bishop}, Publ. Mat., Barc. 37, No. 1, 95--109 (1993; Zbl 0810.30024) Full Text: DOI EuDML