Geodesic
Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces
Serdica Mathematical Journal, Tome 30 (2004) no. 4, pp. 527-548.

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For weakly compact subsets of Hilbert spaces K, we study the existence of totally disconnected spaces L, such that C(K) is isomorphic to C(L). We prove that the space C(BH ) admits a Pełczyński decomposition and we provide a starshaped weakly compact K, subset of BH with non-empty interior in the norm topology, and such that C(K) ~= C(L) with L totally disconnected.
Keywords: C(K) Spaces, Weakly Compact Sets, Regular Averaging Operators, Regular Extension Operators 
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     author = {Argyros, Spiros and Arvanitakis, Alexander},
     title = {Regular {Averaging} and {Regular} {Extension} {Operators} in {Weakly} {Compact} {Subsets} of {Hilbert} {Spaces}},
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Argyros, Spiros; Arvanitakis, Alexander. Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces. Serdica Mathematical Journal, Tome 30 (2004) no. 4, pp. 527-548. http://geodesic.mathdoc.fr/item/SMJ2_2004_30_4_a5/