λ_η-Compact Sets and λ_η-Compact Operators

<strong>Mathematics Seminar of the School of Physical Sciences -------------------------------------------------------------</strong> Title:<strong> λ_η-Compact Sets and λ_η-Compact Operators</strong> Speaker:<strong> Antara Bhar</strong> (National Institute of Science Education &amp; Research, Bhubaneswar) Date: <strong>March 13, 2015</strong> <strong>Abstract: </strong>In this paper, we consider a sequence space λ equipped with the normal topology η (λ, λ^x) and introduce the notion of λ_η-compact sets and λ_η-compact operators. This notion generalizes the work of Sinha and Karn on p-compact sets and p-compact operators. We study the properties of such sets and operators and prove the norm-ideal character of the collection of all λ_η-compact operators. We also establish the connection of λ_η-compact operators with absolutely λ-summing and λ-nuclear operators for suitably chosen sequence space λ.