Electroencephalography-Based Intention Monitoring to Support Nuclear Operators’ Communications for Safety-Relevant Tasks

2021 ◽  
pp. 1-15
Author(s):  
Jung Hwan Kim ◽  
Chul Min Kim ◽  
Yong Hee Lee ◽  
Man-Sung Yim
Keyword(s):  
Nuclear Operators

scholarly journals Operators constructed by means of basic sequences and nuclear matrices

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Ahmed Morsy ◽  
Nashat Faried ◽  
Samy A. Harisa ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Banach Spaces ◽  
Compact Operators ◽  
Schauder Basis ◽  
Countable Number ◽  
Nuclear Operator ◽  
Approximation Numbers ◽  
Infinite Dimensional ◽  
Dimensional Matrix ◽  
Nuclear Operators

AbstractIn this work, we establish an approach to constructing compact operators between arbitrary infinite-dimensional Banach spaces without a Schauder basis. For this purpose, we use a countable number of basic sequences for the sake of verifying the result of Morrell and Retherford. We also use a nuclear operator, represented as an infinite-dimensional matrix defined over the space $\ell _{1}$ℓ1 of all absolutely summable sequences. Examples of nuclear operators over the space $\ell _{1}$ℓ1 are given and used to construct operators over general Banach spaces with specific approximation numbers.

scholarly journals The ideal of Lipschitz classical p-compact operators and its injective hull

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Toufik Tiaiba ◽  
Dahmane Achour
Keyword(s):  
Banach Space ◽  
Compact Operator ◽  
Metric Space ◽  
Metric Spaces ◽  
Compact Operators ◽  
Operator Ideal ◽  
Linear Case ◽  
Injective Hull ◽  
Nuclear Operators ◽  
The Ideal

Abstract We introduce and investigate the injective hull of the strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical p-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi p-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical p-compact operators.

scholarly journals Homological characterizations of the approximation property for Banach spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Yu. V. Selivanov
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Cohomology Group ◽  
Approximation Property ◽  
Three Dimensional ◽  
Nuclear Operators ◽  
Finite Dimensionality

Let E be a Banach space, and let N(E) be the Banach algebra of all nuclear operators on E. In this work, we shall study the homological properties of this algebra. Some of these properties turn out to be equivalent to the (Grothendieck) approximation property for E. These include:(i) biprojectivity of N(E);(ii) biflatness of N(E);(iii) homological finite-dimensionality of N(E);(iv) vanishing of the three-dimensional cohomology group, H3(N(E), N(E)).

Absolutelyp-summing,p-nuclear operators and their conjugates

1973 ◽  
Vol 201 (3) ◽  
pp. 177-200 ◽  
Author(s):  
Joel S. Cohen
Keyword(s):  
Nuclear Operators

scholarly journals Amenability and weak amenability of tensor algebras and algebras of nuclear operators

1991 ◽  
Vol 51 (3) ◽  
pp. 483-488 ◽  
Author(s):  
Niels Grønbaek
Keyword(s):  
Tensor Algebra ◽  
Tensor Algebras ◽  
Canonical Map ◽  
Weak Amenability ◽  
Nuclear Operators ◽  
Finite Dimensional

AbstractLet E and F constitute a Banach pairing. We prove that the algebra of F-nuclear operators on E, Nf (E), is amenable if and only if E is finite dimensional and is weakly amenable if and only if dim KF ≦ 1, and the trace on E⊗F is injective on KF. Here KF is the kernel of the canonical map E⊗^F →NF(E). On the route we find the corresponding statements for the associated tensor algebra, E⊗^F.

Preduals and Nuclear Operators Associated with Bounded, p-Convex, p-Concave and Positive p-Summing Operators

2007 ◽  
Vol 59 (3) ◽  
pp. 614-637 ◽  
Author(s):  
C. C. A. Labuschagne
Keyword(s):  
Banach Spaces ◽  
Positive Operators ◽  
Banach Lattices ◽  
Bounded Operators ◽  
Bounded Linear ◽  
Nuclear Operators ◽  
Linear Maps

AbstractWe use Krivine's form of the Grothendieck inequality to renorm the space of bounded linear maps acting between Banach lattices. We construct preduals and describe the nuclear operators associated with these preduals for this renormed space of bounded operators as well as for the spaces of p-convex, p-concave and positive p-summing operators acting between Banach lattices and Banach spaces. The nuclear operators obtained are described in terms of factorizations through classical Banach spaces via positive operators.

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