Complemented Subspaces of Locally Convex Direct Sum of Banach Spaces

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
A. "Alex" Chigogidze, Professor and Department Chair (Creator)
Institution
The University of North Carolina at Greensboro (UNCG )
Web Site: http://library.uncg.edu/

Abstract: We show that a complemented subspace of a locally convex direct sum of an uncountable collection of Banach spaces is a locally convex direct sum of complemented subspaces of countable subsums. As a corollary we prove that a complemented subspace of a locally convex direct sum of arbitrary collection of l1(Gamma)-spaces is isomorphic to a locally convex direct sum of l1(Gamma)-spaces.

Additional Information

Publication
arXiv:math/0002241v1 [math.FA] 28 Feb 2000
Language: English
Date: 2000
Keywords
Locally convex direct sum, Complemented subspace

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