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Approximation theory in 2-Banach spaces. (English) Zbl 1185.46004
Summary: In order to study approximation theory in 2-Banach spaces, we define the concept of \(T\)-convergence by means of a sequence of linear operators in 2-Banach spaces, and we get some results by imposing the stability and approximation conditions on linear operators. Further, we consider some applications related to the subject.

MSC:
46A70 Saks spaces and their duals (strict topologies, mixed topologies, two-norm spaces, co-Saks spaces, etc.)
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A36 Approximation by positive operators
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