Acta Mathematica Hungarica

, Volume 157, Issue 1, pp 63–79 | Cite as

An isomorphic property in spaces of compact operators and some classes of operators on C(K,X)

  • I GhenciuEmail author


Let \({K_{w^{*}}(X^{*},Y)}\) denote the set of all w*w continuous compact operators from X* to Y. We investigate whether the space \({K_{w^{*}}(X^{*},Y)}\) has property RDP p * (\({1\le p < \infty}\)) when X and \({Y}\) have the same property.

Suppose X and Y are Banach spaces, K is a compact Hausdorff space, \({\Sigma}\) is the \({\sigma}\) -algebra of Borel subsets of K, C(K,X) is the Banach space of all continuous X-valued functions (with the supremum norm), and \({T: C(K,X)\to Y}\) is a strongly bounded operator with representing measure \({m: \Sigma \to L(X,Y)}\).

We show that if T is a strongly bounded operator and \({\hat{T}: B(K, X) \to Y}\) is its extension, then T* is p-convergent if and only if \({\hat{T}^{*}}\) is p-convergent, for \({1\le p < \infty}\).

Key words and phrases

property \({RDP_{p}^{*}}\) space of compact operators p-convergent operator space of continuous functions 

Mathematics Subject Classification

primary 46B20 secondary 46B25 46B28 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of Wisconsin–River FallsWisconsinU.S.A.

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