Let \(X\), \(Y\), and \(Z\) be Banach spaces. The author assumes that there exists a bounded bilinear mapping \(B:X\times Y\rightarrow Z\) such that, for some \(c>0\),
\[ \tfrac1c \| x\| \| y\| \leq\| B(x,y)\| \leq c\| x\| \| y\| , \quad x\in X,\;y\in Y. \]
This is equivalent to the existence of a bounded linear mapping \(L\) from the (completed) projective tensor product \(X\hat\otimes Y\) to \(Z\) such that
\[ \tfrac1c \| x\otimes y\| \leq\| L(x\otimes y)\| \leq c\| x\otimes y\| ,\quad x\in X,\;y\in Y.) \]
A generalization of a basis is considered, namely a sequence \((y_n)\subset Y\) such that, for all \(z\in Z\), there exists a unique sequence \((x_n)\subset X\) such that
\[ z=\sum^\infty_{n=1}B(x_n, y_n). \]
Completeness and minimality of \((y_n)\) are defined in a similar way. Following some introductory facts on the classical counterparts of these notions, similar results on connections between them are obtained.
The paper is not easy to read because of several misprints, language errors, and non-standard notation.