Abstract
In this article, we define a new sequence space generated by the domain of r -Cesàro matrix in Nakano sequence space. Some geometric and topological properties of this sequence space, the multiplication maps defined on it, and the eigenvalue distributions of map ideal with s -numbers that belong to this sequence space have been examined.
Highlights
The vector spaces ltð:Þ are contained in the variable exponent spaces Ltð:Þ
Regarding the 2nd half of the twentieth century, it used to be fulfilled that these variable exponent spaces constituted the proper framework for the mathematical components of numerous issues for which the classical Lebesgue spaces have been inadequate
We evidence the space of all, finite rank, approximable and compact bounded linear maps from a Banach space P into a Banach space Q by
Summary
The vector spaces ltð:Þ are contained in the variable exponent spaces Ltð:Þ. Regarding the 2nd half of the twentieth century, it used to be fulfilled that these variable exponent spaces constituted the proper framework for the mathematical components of numerous issues for which the classical Lebesgue spaces have been inadequate. They explored the quasi Banach ideal of type χtr, for r ∈ ð0, 1 and 1 < t < ∞ They establish its Schauder basis, α − , β − , and γ − duals, and found certain matrix classes connected with this sequence space. V , and we mark it a private sequence space (pss), so as to the class BsV constructs a map ideal This explains a negative answer of Rhoades [32] open problem about the linearity of s-type ðcesðrtÞÞυ spaces. We expound the sufficient setting on ðcesðrtÞÞυ so as to the class of all bounded linear maps which sequence of eigenvalues ðcesðrtÞÞυ equals
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