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Grothendieck's Inequality for JB ∗ ‐Triples and Applications
Author(s) -
Barton T.,
Friedman Y.
Publication year - 1987
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-36.3.513
Subject(s) - dual polyhedron , bilinear interpolation , bounded function , mathematics , factorization , pure mathematics , discrete mathematics , combinatorics , mathematical analysis , statistics , algorithm
There is a universal constant K such that if A and B are JB ∗ ‐triples and V : A × B → C is a bounded bilinear form then there exist norm 1 functionals φε A ∗ and ψε B ∗ and corresponding pre‐Hilbertian seminorms ∥ · ∥ ø and ∥ · ∥ ψ such that | V ( x , y )| ⩽ K ∥ V ∥ ∥ x ∥ φ ∥ y ∥ ψ for all x ε A and y ε B . It follows that duals of JB ∗ ‐triples have cotype 2 and that bounded linear operators from a JB ∗ ‐triple to the dual of another JB ∗ ‐triple factorize through Hilbert spaces.