Dieudonné-Schwartz theorem on bounded sets in inductive limits. II

Abstract

The Dieudonné-Schwartz Theorem [<bold>1</bold>, Chapter 2, §12] has been stated for strict inductive limits. In [<bold>3</bold>] it has been extended to inductive limits. Here the result of [<bold>3</bold>] is generalized. Also, the case when each set bounded in ind lim <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E Subscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{E_n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is contained, but not necessarily bounded, in some <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E Subscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>E</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{E_n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is considered.

Locations

• Proceedings of the American Mathematical Society - View - PDF