Diagonals of projective tensor products and orthogonally additive polynomials

• Autorzy: Qingying Bu , Gerard Buskes
• Języki publikacji: EN

Abstrakty

EN

Let E be a Banach space with 1-unconditional basis. Denote by $Δ(⊗̂_{n,π}E)$ (resp. $Δ(⊗̂_{n,s,π}E)$) the main diagonal space of the n-fold full (resp. symmetric) projective Banach space tensor product, and denote by $Δ(⊗̂_{n,|π|}E)$ (resp. $Δ(⊗̂_{n,s,|π|}E)$) the main diagonal space of the n-fold full (resp. symmetric) projective Banach lattice tensor product. We show that these four main diagonal spaces are pairwise isometrically isomorphic, and in addition, that they are isometrically lattice isomorphic to $E_{[n]}$, the completion of the n-concavification of E. Using these isometries, we also show that the norm of any (vector valued) continuous orthogonally additive homogeneous polynomial on E equals the norm of its associated symmetric linear operator.

Kategorie tematyczne

• 46G25: (Spaces of) multilinear mappings, polynomials
• 46B28: Spaces of operators; tensor products; approximation properties
• 47H60: Multilinear and polynomial operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2014
• Tom: 221
• Numer: 2
• Strony: 101-115

Daty

wydano

2014

Twórcy

autor

Qingying Bu

• Department of Mathematics, University of Mississippi, University, MS 38677, U.S.A.

autor

Gerard Buskes

• Department of Mathematics, University of Mississippi, University, MS 38677, U.S.A.

Identyfikatory

DOI

10.4064/sm221-2-1