Existence of the normalized B-basis and a practical construction method of the B-algorithm

Necessary and sufficient conditions for the existence of a normalized B-basis on an extended Chebyshev space are presented. A method for constructing a normalized B-basis is given and the symmetry of the normalized B-basis is proved. Furthermore, a practical construction method for the B-algorithm on an extended Chebyshev space is discussed. Normalized B-bases and B-algorithms on some function spaces are also given.