Equality of two strongly unique minimal projection constants

Abstract

Let P(X, Y ) denote the set of all linear, continuous projections from a Banach space X onto a linear subspace Y . Letf = ( f 1 , .

A note on generalized projections in c0

“…Also formulas for the relative generalized projection constant λ Z (V, X) and the strong uniqueness constant will be given. This generalizes some results of J. Blatter and E. W. Cheney [3] and G. Lewicki and A. Micek [19]. Our results seem interesting because cases in which exact values of the above constants can be given are rare.…”

“…For results concerning strong uniqueness in general and in the context of minimal projections see e.g. [1], [2], [18], [19], [23], [24], [26], [28], [32].…”

Codimension-one minimal extensions onto Haar subspaces

“…For 0 < |l| < 2|k| consider an operator A k,l : P 2 [−1, 1] ∋ bt 2 + ct + d  → kbt 2 + lct + kd ∈ P 2 [−1, 1]. Observe that an isomorphismà k,l : P 3 [−1, 1] → P 3 [−1, 1] given by the formulã A k,l (at 3 + bt 2 + ct + d) = lat 3 + kbt 2 + lct + kd (18) belongs to the spaceW k,l and it can be written as…”

“…Basic information about minimal projections and extensions one can find in [1,[4][5][6]9,10,15,16,18,21,22]. Let W be a Banach space and V its closed linear subspace.…”