Affiliation:
1. Ivan Franko National University of Lviv, Ukraine + Jan Kochanowski University in Kielce, Poland
2. Department of Mathematics, Ben-Gurion University of the Negev, Israel
Abstract
Let L(X) be the free locally convex space over a Tychonoff space X. We prove
that the following assertions are equivalent: (i) every functionally bounded
subset of X is finite, (ii) L(X) is semi-reflexive, (iii) L(X) has the
Grothendieck property, (iv) L(X) is semi-Montel. We characterize those
spaces X, for which L(X) is c0-quasibarrelled, distinguished or a (d f)-space. If X is a convergent sequence, then L(X) has the Glicksberg
property, but the space L(X) endowed with its Mackey topology does not have
the Schur property.
Publisher
National Library of Serbia
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