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Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations pp 185–218Cite as

Application to Compact Matrix Operators

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Abstract

In this chapter, we present some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators given by infinite matrices that map an arbitrary BK space into the sequence spaces \(c_{0}\), \(c\), \(\ell _{\infty }\) and \(\ell _{1}\), and into the matrix domains of triangles in these spaces. It is shown that many linear compact operators may be represented as matrix operators in sequence spaces or integral operators in function spaces.

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Authors and Affiliations

  1. Department of Mathematics, Rzeszów University of Technology, al. Powstańców Warszawy 8, 35-959, Rzeszow, Poland

    Józef Banaś

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, Uttar Pradesh, India

    Mohammad Mursaleen

Authors
  1. Józef Banaś
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  2. Mohammad Mursaleen
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Correspondence to Józef Banaś .

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Banaś, J., Mursaleen, M. (2014). Application to Compact Matrix Operators. In: Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1886-9_6

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