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Jan Baars ) JA  EA=H =FFECI >AJMAA BK?JE IF=?AI

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Jan Baars

A note on linear mappings between function spaces

Comment.Math.Univ.Carolinae 34,4 (1993) 711-715.

Abstract: Arhangel’skiˇı proved that ifXandY are completely regular spaces such thatCp(X) andCp(Y) are linearly homeomorphic, thenX is pseudocompact if and only ifY is pseudocompact. In addition he proved the same result for compactness, σ-compactness and realcompactness. In this paper we prove that if φ:Cp(X)→ Cp(Y) is a continuous linear surjection, thenY is pseudocompact providedXis and ifφis a continuous linear injection, thenXis pseudocompact providedY is. We also give examples that both statements do not hold for compactness, σ-compactness and realcompactness.

Keywords: function space, topology of pointwise convergence AMS Subject Classification: 54C35, 57N17

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