Multiple Tensor Norms of Michor’s Type and Associated Operator Ideals

2019 ◽  
pp. 191-224
Author(s):  
Juan Antonio López Molina
Keyword(s):  
Operator Ideals ◽  
Tensor Norms

On the Maximal Operator Ideal Associated with a Tensor Norm Defined by Interpolation Spaces

2010 ◽  
Vol 53 (4) ◽  
pp. 690-705
Author(s):  
M. E. Puerta ◽  
G. Loaiza
Keyword(s):  
Maximal Operator ◽  
Interpolation Space ◽  
Sufficient Conditions ◽  
Classical Approach ◽  
Operator Ideals ◽  
Metric Properties ◽  
Real Method ◽  
Tensor Norm ◽  
Tensor Norms ◽  
Necessary And Sufficient

AbstractThe classical approach to studying operator ideals using tensor norms mainly focuses on those tensor norms and operator ideals defined by means of ℓp spaces. In a previous paper, an interpolation space, defined via the real method and using ℓp spaces, was used to define a tensor norm, and the associated minimal operator ideals were characterized. In this paper, the next natural step is taken, that is, the corresponding maximal operator ideals are characterized. As an application, necessary and sufficient conditions for the coincidence of the maximal and minimal ideals are given. Finally, the previous results are used in order to find some new metric properties of the mentioned tensor norm.

scholarly journals Approximation properties of tensor norms and operator ideals for Banach spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 1698-1708
Author(s):  
Ju Myung Kim
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Approximation Property ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Finitely Generated ◽  
Tensor Norm ◽  
Tensor Norms

Abstract For a finitely generated tensor norm α \alpha , we investigate the α \alpha -approximation property ( α \alpha -AP) and the bounded α \alpha -approximation property (bounded α \alpha -AP) in terms of some approximation properties of operator ideals. We prove that a Banach space X has the λ \lambda -bounded α p , q {\alpha }_{p,q} -AP ( 1 ≤ p , q ≤ ∞ , 1 / p + 1 / q ≥ 1 ) (1\le p,q\le \infty ,1/p+1/q\ge 1) if it has the λ \lambda -bounded g p {g}_{p} -AP. As a consequence, it follows that if a Banach space X has the λ \lambda -bounded g p {g}_{p} -AP, then X has the λ \lambda -bounded w p {w}_{p} -AP.

scholarly journals Operator ideals and tensor norms defined by a sequence space

2004 ◽  
Vol 69 (3) ◽  
pp. 499-517 ◽  
Author(s):  
J.A. López Molina ◽  
M.J. Rivera
Keyword(s):  
Classical Theory ◽  
Sequence Space ◽  
Maximal Operator ◽  
Dimensional Structure ◽  
Operator Ideals ◽  
Finite Dimensional ◽  
Tensor Norm ◽  
Tensor Norms

We study the tensor norm defined by a sequence space λ and its minimal and maximal operator ideals associated in the sense of Defant and Floret. Our results extend the classical theory related to the tensor norms of Saphar [16]. They show the key role played by the finite dimensional structure of the ultrapowers of λ in this kind of problems.

scholarly journals (n + 1)-TENSOR NORMS OF LAPRESTÉ'S TYPE

2012 ◽  
Vol 54 (3) ◽  
pp. 665-692 ◽  
Author(s):  
J. A. LÓPEZ MOLINA
Keyword(s):  
Linear Operator ◽  
Tensor Product ◽  
Tensor Products ◽  
Operator Ideals ◽  
Tensor Norm ◽  
Tensor Norms

AbstractWe study an (n + 1)-tensor norm αr extending to (n + 1)-fold tensor products, the classical one of Lapresté in the case n = 1. We characterise the maps of the minimal and the maximal multi-linear operator ideals related to αr in the sense of Defant and Floret (A. Defant and K. Floret, Tensor norms and operator ideals, North Holland Mathematical Studies, no. 176 (North Holland, Amsterdam, Netherlands, 1993). As an application we give a complete description of the reflexivity of the αr-tensor product (⊗j = 1n + 1 ℓuj, αr).

Injective Dual Banach Spaces and Operator Ideals

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Raffaella Cilia ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Spaces ◽  
Operator Ideals
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