When is the sum of complemented subspaces complemented?

2016/06/26 by Feshchenko, Ivan
#46N30 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B99 #Secondary 46B28

paper · doi:10.48550/arxiv.1606.08048

Abstract

We provide a sufficient condition for the sum of a finite number of complemented subspaces of a Banach space to be complemented. Under this condition a formula for a projection onto the sum is given. We also show that the condition is sharp (in a certain sense). As applications, we get (1) sufficient conditions for the complementability of sums of marginal subspaces in L^p and sums of tensor powers of subspaces in a tensor power of a Banach space and (2) quantitative results on stability of the complementability property of the sum of linearly independent subspaces.

Related

• Complemented subspaces of J-sums of Banach spaces
• Complemented subspaces of products of Banach spaces
• Complemented subspaces of locally convex direct sums of Banach spaces
• Complemented subspaces of Banach lattices
• Complemented Subspaces of L_p Determined by Partitions and Weights