Displaying similar documents to “A characterization of regular averaging operators and its consequences”

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

Argyros, Spiros, Arvanitakis, Alexander (2004)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20. 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. Research partially...

Regular spaces of small extent are ω-resolvable

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2015)

Fundamenta Mathematicae

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We improve some results of Pavlov and Filatova, concerning a problem of Malykhin, by showing that every regular space X that satisfies Δ(X) > e(X) is ω-resolvable. Here Δ(X), the dispersion character of X, is the smallest size of a non-empty open set in X, and e(X), the extent of X, is the supremum of the sizes of all closed-and-discrete subsets of X. In particular, regular Lindelöf spaces of uncountable dispersion character are ω-resolvable. We also prove that...