Premium
Closure of Cones in Completed Injective Tensor Products
Author(s) -
Alcántara Julio
Publication year - 1983
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/s2-28.3.551
Subject(s) - injective function , tensor product , mathematics , banach space , separable space , closure (psychology) , pure mathematics , dual space , regular polygon , combinatorics , mathematical analysis , geometry , economics , market economy
Suppose that E is a complex locally convex space equipped with a continuous involution, ∗ . We consider the cone of finite sums of positive elements( E ⊗ E ) + = {∑ i = 1 n f i ∗ ⊗ f 1 : f 1 ∈ E , 1 ⩽ i ⩽ n , n ∈ ℕ }in the completed injective tensor product E⊗ ˜E . Then if E = E 1 ⊕ E 2 where E 1 is a Fréchet space and E 2 is a complete space whose strong dual is barrelled and such that every continuous linear map from the strong dual into any Banach space has separable range, then the closure of ( E ⊗ E ) + in E⊗ ˜E is exactly the set of convergent infinite sums of positive elements.