Orthogonality of analytic polynomials: a little step further

From the constellation mentioned in Jones and Njåstad (J. Comput. Appl. Math. 105 (1999) 51–91) we have chosen orthogonality of polynomials and moment problems enriching them with operator theory apparatus. Thus this essay resumes the theme of Szafraniec (J. Comput. Appl. Math. 49 (1993) 255) and culminates in updating it with the results of Stochel and Szafraniec (J. Funct. Anal. 159 (1998) 432).