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The spectrum of mapping ideals of type variable exponent function space of complex variables with some applications. (English) Zbl 1495.47041

Summary: The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by \(s\)-numbers and this function space of complex variables, are investigated in this article. Upper bounds for \(s\)-numbers of infinite series of the weighted \(n\)th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions.

MSC:

47B06 Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
47L20 Operator ideals
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