Remarks on Spaces of Compact Operators between Reflexive Banach Spaces

2014 ◽  
pp. 189-194
Author(s):  
G. Godefroy
Keyword(s):  
Banach Spaces ◽  
Compact Operators ◽  
Reflexive Banach Spaces

scholarly journals Spaces of compact operators which areM-ideals inL(X,Y)

1992 ◽  
Vol 15 (3) ◽  
pp. 617-619
Author(s):  
Chong-Man Cho
Keyword(s):  
Banach Spaces ◽  
Dual Space ◽  
Compact Operators ◽  
Linear Operators ◽  
Reflexive Banach Spaces ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Second Dual

SupposeXandYare reflexive Banach spaces. IfK(X,Y), the space of all compact linear operaters fromXtoYis anM-ideal inL(X,Y), the space of all bounded linear operators fromXtoY, then the second dual spaceK(X,Y)**ofK(X,Y)is isometrically isomorphic toL(X,Y).

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 index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces

2005 ◽  
Vol 214 (1) ◽  
pp. 189-231 ◽  
Author(s):  
Athanassios G. Kartsatos ◽  
Igor V. Skrypnik ◽  
Vladimir N. Shramenko
Keyword(s):  
Critical Point ◽  
Banach Spaces ◽  
Elliptic Operators ◽  
Reflexive Banach Spaces
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