Some Results on Absolute Projection Constants. (2nd January 2019)

• Record Type: Journal Article
• Authors: Castejón, Alberto; Lewicki, Grzegorz; Martín, Alberto
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 1(2019)
• Page Start: 34
• Page End: 51
• Publication Date: 2019-01-02
• Subjects: Absolute projection constant -- minimal projection -- symmetric matrices -- Hermitian matrices -- unitary matrices -- eigenvalues -- eigenvectors; 46A22 -- 47A30 -- 47A58; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1486327
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Let V be an n -dimensional real or complex Banach space and letλ ( V ) denote its absolute projection constant. For anyN ∈ N, N ≥ n defineλ n N = sup { λ ( V ) : d i m ( V ) = n, V ⊂ l ∞ ( N ) } . In this article, we determine, in the complex case, minimal projections with respect to l 1 -norm as well as with respect tol ∞ -norm for subspaces given by solutions of certain extremal problems. As an application we show that for anyn, N ∈ N, N ≥ n, there exists an n -dimensional subspaceV n ⊂ l 1 ( N ) such thatλ n N = λ ( V n, l 1 ( N ) ) . This generalizes the results from Castejon and Lewicki (2014) obtained in the real case.