New examples of weakly compact approximation in Banach spaces.
Weak essential spectra of multiplication operators on spaces of bounded linear operators.
Weak Compactness of Multiplication Operators on Spaces of Bounded Linear Operators.
Representing non-weakly compact operators
For each S ∈ L(E) (with E a Banach space) the operator R(S) ∈ L(E**/E) is defined by R(S)(x** + E) = S**x** + E(x** ∈ E**). We study mapping properties of the correspondence S → R(S), which provides a representation R of the weak Calkin algebra L(E)/W(E) (here W(E) denotes the weakly compact operators on E). Our results display strongly varying behaviour of R. For instance, there are no non-zero compact operators in Im(R) in the case of and C(0,1), but R(L(E)/W(E)) identifies isometrically with...
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