Abstract Köthe spaces. IV

1968 ◽  
Vol 64 (1) ◽  
pp. 45-52
Author(s):  
D. H. Fremlin
Keyword(s):  
Tensor Product ◽  
Function Space ◽  
Function Spaces ◽  
Riesz Space ◽  
Natural Order ◽  
Order Structure ◽  
Topological Properties ◽  
Projective Tensor Product ◽  
Köthe Spaces ◽  
Projective Tensor

In this paper I investigate the completed projective tensor product of two perfect Riesz spaces, and show how a natural order structure on this renders it also a perfect Riesz space. Sections 7–14 contain interesting order-topological properties of this tensor product. Finally, section 15 describes how the tensor product of function spaces may be represented as a function space, in the manner of (1 b).

Abstract Köthe spaces. III

1967 ◽  
Vol 63 (4) ◽  
pp. 957-962 ◽  
Author(s):  
D. H. Fremlin
Keyword(s):  
Natural Order ◽  
Fundamental Result ◽  
Order Structure ◽  
Continuous Linear ◽  
Topological Properties ◽  
Riesz Spaces ◽  
Köthe Spaces ◽  
Linear Maps ◽  
Special Cases ◽  
Special Case

In this paper I shall be considering the space of linear maps between two (perfect) Riesz spaces, and shall show how certain topological properties of these maps are related to the natural order structure of the space. The fundamental result is (e) of section 4, certain special cases of which have been treated in (4) and (5), using a less elliptic method of proof. Probably the most interesting new result in the present paper is section 10 in the special case of both L and M× being L1 spaces (so that |σ| (L, L×) and |σ| (M×, M) are the norm topologies ((2 b), section 7) and Λ(L; M×) is the space of norm-continuous linear maps).

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

scholarly journals SUBPROJECTIVITY OF PROJECTIVE TENSOR PRODUCTS OF BANACH SPACES OF CONTINUOUS FUNCTIONS

2021 ◽  
pp. 1-14
Author(s):  
R.M. CAUSEY
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Tensor Products ◽  
Continuous Functions ◽  
Hausdorff Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
Spaces Of Continuous Functions

Abstract Galego and Samuel showed that if K, L are metrizable, compact, Hausdorff spaces, then $C(K)\widehat{\otimes}_\pi C(L)$ is c0-saturated if and only if it is subprojective if and only if K and L are both scattered. We remove the hypothesis of metrizability from their result and extend it from the case of the twofold projective tensor product to the general n-fold projective tensor product to show that for any $n\in\mathbb{N}$ and compact, Hausdorff spaces K1, …, K n , $\widehat{\otimes}_{\pi, i=1}^n C(K_i)$ is c0-saturated if and only if it is subprojective if and only if each K i is scattered.

scholarly journals Types of Radon-Nikodym properties for the projective tensor product of Banach spaces

2003 ◽  
Vol 47 (4) ◽  
pp. 1303-1326 ◽  
Author(s):  
Qingying Bu ◽  
Joe Diestel ◽  
Patrick Dowling ◽  
Eve Oja
Keyword(s):  
Tensor Product ◽  
Banach Spaces ◽  
Projective Tensor Product ◽  
Projective Tensor

Johnson pseudo-contractibility of second duals of certain Banach algebras

2019 ◽  
pp. 2150012
Author(s):  
A. Sahami ◽  
E. Ghaderi ◽  
S. M. Kazemi Torbaghan ◽  
B. Olfatian Gillan
Keyword(s):  
Tensor Product ◽  
Matrix Algebra ◽  
Banach Algebras ◽  
Amenable Group ◽  
Semigroup Algebra ◽  
Archimedean Semigroup ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
The Matrix ◽  
Second Dual

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

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