Diagonals of projective tensor products and orthogonally additive polynomials

Qingying Bu, and Gerard Buskes. "Diagonals of projective tensor products and orthogonally additive polynomials." Studia Mathematica 221.2 (2014): 101-115. <http://eudml.org/doc/285830>.

@article{QingyingBu2014,
abstract = {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.},
author = {Qingying Bu, Gerard Buskes},
journal = {Studia Mathematica},
keywords = {projective tensor product; diagonal; concavification; orthogonally additive polynomials},
language = {eng},
number = {2},
pages = {101-115},
title = {Diagonals of projective tensor products and orthogonally additive polynomials},
url = {http://eudml.org/doc/285830},
volume = {221},
year = {2014},
}

TY - JOUR
AU - Qingying Bu
AU - Gerard Buskes
TI - Diagonals of projective tensor products and orthogonally additive polynomials
JO - Studia Mathematica
PY - 2014
VL - 221
IS - 2
SP - 101
EP - 115
AB - 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.
LA - eng
KW - projective tensor product; diagonal; concavification; orthogonally additive polynomials
UR - http://eudml.org/doc/285830
ER -