Abstract
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.
Highlights
Operator ideal theory has various applications in the geometry of Banach spaces, xed point theory, spectral theory, and other areas of mathematics, among other areas of knowledge
Sv: the operator ideals formed by the sequence of s -numbers in any sequence space V
SaVpp: the operator ideals formed by the sequence of approximation numbers in any sequence space V
Summary
Operator ideal theory has various applications in the geometry of Banach spaces, xed point theory, spectral theory, and other areas of mathematics, among other areas of knowledge. Sv: the operator ideals formed by the sequence of s -numbers in any sequence space V. SaVpp: the operator ideals formed by the sequence of approximation numbers in any sequence space V. Several operator ideals in the class of Banach or Hilbert spaces are defined by sequences of real numbers. Faried et al [9] introduced the upper bounds for s-numbers of infinite series of the weighted nth power forward shift operator on H rððbaÞÞ, for 1 ≤ r < ∞, with some applications to some entire functions. We introduce the sufficient conditions on H pð:Þ to generate premodular special space of formal power series. ÐHpð:ÞÞρ In Section 5, we estimate the upper bounds for s-numbers of infinite series of the weighted nth power forward and backward shift operator on H pð:Þ with approaches to some entire functions We show the smallness of S . ðHpð:ÞÞρ Fifthly, we investigate the simpleness of S . ðHpð:ÞÞρ Sixthly, we present the enough setup on ðH pð:ÞÞρ such that the class L with its sequence of eigenvalues in ðH pð:ÞÞρ equals S . ðHpð:ÞÞρ In Section 5, we estimate the upper bounds for s-numbers of infinite series of the weighted nth power forward and backward shift operator on H pð:Þ with approaches to some entire functions
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