On Generalized Approximative Properties of Systems

Theory of classical basis including Schauder basis is sufficiently well developed, and quite a good number of monographs such as Day 1 , Singer 2, 3 , Young 4 , Bilalov, Veliyev 5 , Ch. Heil 6 , and so forth have been dedicated to it so far. There are different versions and generalizations of the concept of classical basis for more details see 2, 3 . One of such generalizations is proposed in 5, 7 . In these works, the concept of bY -invariance is first introduced and then used to obtain main results. It should be noted that the condition of bY -invariance implies the fact that the corresponding mapping is tensorial. In our work, we neglect the bY -invariance condition. We give more detailed consideration to the space of coefficients. We also state a criterion of basicity.