Abstract
In this paper, we introduce the grand Lorentz sequence spaces l_{p,q)}^{θ} and study on some topological properties. Also, we characterize some properties of the multiplication operator, such as compactness, Fredholmness etc., defined on l_{p,q)}^{θ}.
Highlights
Let (X; S; ) be a ...nite measure space and let g be a complex-valued measurable function de...ned on X
We introduce the grand Lorentz sequence spacesp;q) and study on some topological properties
We characterize some properties of the multiplication operator, such as compactness, Fredholmness etc., de...ned onp;q)
Summary
Let (X; S; ) be a ...nite measure space and let g be a complex-valued measurable function de...ned on X. We introduce the grand Lorentz sequence spacesp;q) and study on some topological properties. If is counting measure on S = 2N, we can write the distribution function and the non-increasing rearrangement of a complex-valued sequence (xn), respectively, as follows; F (t) = fn 2 N : jxnj > tg ; t 0 and x (n) = inf ft > 0 : F (t) n 1g if n 1 t < n with F (t) < 1. Grand Lorentz sequence spaces, multiplication operator, compactness, Fredholm operator.
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