COMPACT MATRIX OPERATORS BETWEEN THE SPACES m(ϕ), n(ϕ) AND ℓp

Title & Authors
COMPACT MATRIX OPERATORS BETWEEN THE SPACES m(ϕ), n(ϕ) AND ℓp

Abstract
We give the characterizations of the classes of matrix trans-formations ($\small{m(\phi),{\ell}_p}$), ($\small{n(\phi),{\ell}_p}$) ([5, Theorem 2]), ($\small{{\ell}_p,m(\phi)}$) ([5, Theorem 1]) and ($\small{{\ell}_p,n(\phi)}$) for $\small{1{\leq}p{\leq}{\infty}}$, establish estimates for the norms of the bounded linear operators defined by those matrix transformations and characterize the corresponding subclasses of compact matrix operators.
Keywords
sequence spaces;matrix transformations;compact operators;Hausdorff measure of noncompactness;
Language
English
Cited by
1.
RETRACTED: The Hausdorff measure of noncompactness for some matrix operators, Nonlinear Analysis: Theory, Methods & Applications, 2013, 92, 119
2.
Infinite System of Differential Equations in Some Spaces, Abstract and Applied Analysis, 2012, 2012, 1
3.
On the mth order difference sequence space of generalized weighted mean and compact operators, Acta Mathematica Scientia, 2013, 33, 3, 797
4.
Applications of Measure of Noncompactness in Matrix Operators on Some Sequence Spaces, Abstract and Applied Analysis, 2012, 2012, 1
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