Abstract
It is proved that the arbitrary nondegenerate system in a linear complete topological space has a correspondence complete topological space of coefficients with canonical basis. Basicity criterion for systems in such spaces is given in terms of coefficient operator.
Highlights
The concept of the space of coefficients belongs to the theory of bases
It is proved that the arbitrary nondegenerate system in a linear complete topological space has a correspondence complete topological space of coefficients with canonical basis
Basicity criterion for systems in such spaces is given in terms of coefficient operator
Summary
The concept of the space of coefficients belongs to the theory of bases. As is known, every basis in a Banach space has a Banach space of coefficients which is isomorphic to an initial one (see, e.g., Dremin, Ivanov, & Nechitailo, 2001; Singer, 1970; Singer, 1981). Every nondegenerate system (to be defined later) in a Banach space generates the corresponding Banach space of coefficients with canonical basis (see, e.g., Bilalov & Najafov, 2011; Dremin, Ivanov, & Nechitailo, 2001). Space of coefficients plays an important role in the study of approximative properties of systems It has very important applications in various fields of science, such as solid body physics, molecular physics, multiple production of particles, aviation, medicine, biology, data compression, etc (see, e.g., Chui, 1992; Edwards, 1969 and references within). Our work is dedicated to the study of topological properties of the space of coefficients generated by nondegenerate system in a Hausdorff linear topological spaces Basicity criterion for systems in such spaces is given in terms of coefficient operator
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